If you want to stay in Ukraine with your wife. Go to the Ukrainian Embassy in England and obtain a Visa D. It is a 45 temporary visa. Make sure all of your documents are accurate, and I mean precise, Your marriage certificate has to be certified in Ukraine.and apostille here in Ukraine. In the city she lives they can do that or a service can provide that service for you. When you get to Ukraine you will need to go with your wife and start the process of obtaining a one year temporary visa. You can come and go on that visa and you will be able to obtain an internal passport which allows you to reside in the country. Before the one year visa expires you will need to apply for another one year visa. After two years of marriage you will be able to apply and receive a permanent resident visa.
The clock is ticking so apply for the one year visa prior to your 45 Visa D expiring. It is madness, but your wife being Ukrainian knows how the system works. When I did the process, I just let my wife do the talking and I just stayed quiet. She may be required to make a donation at the local internal passport office. So let her talk and keep quiet. Do not disrupt the system, it is the way things work. People have all different experiences, but I will tell you, let your wife talk to the locals.
I applied for my one year within a one week period of obtaining my Visa D and returning to Ukraine. I did not have a bad experience besides the waiting. But my wife took care of everything.
For my own experience it is different. I am an American. I was coming to Kharkov to Marry my wife. She found out all of the documents I need to bring with me from California. I arrived at the airport and received the 90 stamp in my passport. We got married and prior to my 90 day period being expired we took all of our documents to Moldova to the Ukrainian Embassy and received my Visa D. It was a crazy chance for if anything was wrong I would have had to return to the U.S. to get my documents. But I made sure I had everything done correctly and received my Visa D in one day. We returned to Kharkov and we went to the Internal passport office and submitted our documents. Do your research, and have your wife double check all documents you need and what is required. At one point we had to supply my wife owned a flat and it was my resident while I lived here.
Double check all that is required, make sure all of your documents are correct. Make sure your documents match your name exactly in your British Passport. Anything you Apostille in England, make sure you bring two of each document Apostille, just in case they lose anything.
Good Luck and I wish you happiness with your new bride. I have been happily married for many years with my wife, best thing I ever did was to marry my sweet wife. Things are different here than where we came from. So let your wife teach you about Ukraine, enjoy her family and the friends you will make.