One thing you should check right now, even before you consider purchasing, is to see if your credit file is OK. Sometimes, it might be missing information (e.g. electoral roll registration) or misinformation (e.g. fraud credit) that will harm your chances of getting a mortgage. You want to get it sorted ASAP.
Request your statutory credit file from Experian as a first step (should be free or £2, don't get persuaded to sign up for their monthly/annual plan).
Also sign up for Noddle, a free credit file service. They will send you notifications every time there is a change to your credit file, so you can monitor and make sure nothing mistaken happens to it.
It looks like you don't have British citizenship. If you are here on a visa, that would make it more tricky to get a mortgage. Most lenders will insist on at least 2 years left on your mortgage, at the time of application, and many lenders don't lend to visa holders at all. If you are EU citizen, I'm not sure what the banks are thinking post-Brexit. My advice would be just go talk to your mortgage advisor in your current bank, in person, just to see what their policies are, they will probably also be able to advise what general industry practices are with regards to mortgages to foreign residents.