Getting an Azerbaijani visa is no easy task and as such I did lots of googling before my travels and spoke to lots of like minded travellers who gave me plenty of tips along the way. Beforehand I had come across Batumi, Georgia being the best place to acquire one (as I'm guessing you have) but could find very little information on the process, chance of success and importantly as my budget was small the costs of obtaining one. As such now I have been to Batumi, Georgia and acquired the visa I thought I'd provide this page with as much information as possible to make it a bit easier for you.
Now in Batumi, Georgia you must go to the Azerbaijani embassy (consulate). It opens at 10am monday to friday (excl holiday days). The embassy is at 14, Nodar Dumbadze str this is very central in Batumi, Georgia and easy to find. You need to show the security guard your passport and explain your reason for wishing to enter the consulate ie visa and he will add you to a list and get you an appointment. I had to wait about 20 minutes for entry and most people appeared to wait around this sort of time never much longer. Once inside the gentleman who runs the consulate speaks very good english. He is the chap who issues the visa. You will need to explain why you wish to enter Azerbaijan (tourism is fine) and he asks general questions about your visit where you've been and why you wish to go to Azerbaijan etc.
You then have to fill in an application form - very standard stuff about you personally. There is a bit on who has invited you to Azerbaijan ere (I'm guessing you've read about this requirement) simply leave this blank. My understanding is that he is inviting us as a member of the Azerbaijani government but he did not make this clear and I didn't push it. But crucially no letter of invitation is required!! This is a major bonus and I'm guessing why you've been looking into Batumi , Georgia for the visa. All you need is your passport plus 2 passport photos, and 2 photocopies of your passport. It takes 3 whole working days to get the visa (excl the day you went to the office) so bear this in mind. Now very handily you get to keep your passport so can use this time to travel around or stay in Batumi. Batumi is a nice holiday resort, however after a day we used the time to rent a car and see more of Georgia.
Now in the questioning at the consulate the obvious questions about the disputed Azerbaijan/ Armenia territory were asked - it is a certainty that you will not get a visa if you have visited the disputed area, however, if you have just been to Armenia he made it clear he could still grant the visa. I would however say when making the trip across I heard numerous stories of people having problems on the border if you have an Armenian stamp, however, someone on the train had one and was allowed entry but it just caused further questioning and searching but was not a bar to entry. I had not gone to Armenia so cannot say for certain what will happen to UK nationals but I do not think it will be a problem.
Unfortunately although the process is simple and crucially the letter of invitation not required - the visa is expensive. As a UK national it was 210 Georgian lari (at time of writing about 85 pound). Now again based on speaking to people on the train German citizens paid roughly 55 euros. But bar that I do not know. The price was not stated anywhere he appeared to just pluck it out of the air. I do know however, that Canadians and USA citizens can get visas here as I saw the processed applications (cannot comment on cost).
Oh in case the time it takes is a real concern he can do it next day - however, this is double the cost. When we turned back up to collect the visa, he did it by hand in front of us so no idea why it takes so long on standard application but guessing that's how he can do it next day if you are willing to pay.
I hope this was helpful please comment if you want any more information I will be more than happy to help if I can.
In case you are also wondering a bit about travel from Georgia to Azerbaijan. I can provide some information on this as well. From Batumi to Tbilisi I took a marshutkas - they are in reality a minivan and are very popular for transport in Georgia Go to the main station and buy it from the office which has Tbilisi written outside ( I found this one best value as it is a fixed price). It was 20 lari (about 8 pounds). It left at 11.30pm arrived at 7am in Tbilisi - I chose overnight to save a hostel fee but they ran often and there is a lot of choice. Just to warn you this was one of the most uncomfortable journeys of my life and I've done a fair amount of travelling - the seats are so cramped and the Georgian customers put their seats right back restricting movement even more. But it is good value and quite quick so your choice.
When in Tbilisi I recommend going straight to the train station ( the marshutkas drops you right outside). If you got there another way no 37 bus (again a minivan) goes there from Rustaveli street (the main one - you'll know it when your there) - a ticket costs 0.50 lari. In the train station go up to any occupied booth and ask if they speak English (assuming you can't speak Georgian or Russian) they either will or will tell you a booth number that does and then simply ask for a ticket to Baku. There are 3 classes on the train - the reason I said go straight away is that the train sells out. I wanted next day and only 3rd class was left. Now this is upto you but 3rd class was fine - you get a bed its comfy but its just a dorm style and no privacy. 2nd class had private rooms, I didn't get to see 1st but I'm guessing just better beds etc. Price for 3rd class was 37 lari ( about £15).
The train leaves at 4.30pm everyday and arrives in Baku at 10am. The train journey itself is uneventful bar the border crossing. This is slow and quite eventful. You firstly stop after about 2 hours on the train at Georgian border. Passports are taken by officer - and brought back about 40 mins later with exit stamp. A few questions were asked but very trivial. Everyone just waits outside the train buys drinks from a little stall and smokes. You then go about 40 mins further and you get to Azerbaijan border. This is more serious. By this point the staff have already given you a customs form (its in English and very simple). Armed officers enter the train with customs people. As a foreigner we were quickly earmarked and had a senior officer take our passports and ask us numerous questions - these were pleasant and the questions mainly concerned money and our bags. Some people were invited for further questioning - I cannot tell you what this was based on I'm guessing just random. Bags and people were searched (both locals and foreigners). You are then photo'd and a few more questions were asked then the visa stamped and that is all you are past the border and then nothing until arrival in Baku.
I would hasten to add there is no visa possibility at the border ( 2 other foreigners were on train without visas with intention of purchasing at the border but upon realisation of no visa they were removed from the train).
Again hope this information helped. Please ask questions and I will endeavor help if I can.