If you can go to the western part of the country visit Brest and Grodno. Brest is the place where Great Patriotic War began, Brest Hero Fortress is a sacred place of all Soviet Union. Also you can visit trains museum and museum of saved values (cultural values confiscated from illegal transporters). Grodno is the most medieval city of Belarus.

I know that you want to see military parade on 9 May. But I don't know if it is a good idea. There will be huge crowd of people and security measures. We had a bomb blow in underground in April so I think security measures will be increased.

You can see "Stalin's line" historical complex of WWII, renovated part of Minsk fortified region.

Border control. Sorry but I think they just never or rarely saw UK passport, you should know that there are no border between Russia and Belarus, and border guard catches many illegal people with fake passports (even I saw passport of the citizen of the world ) every day. Belarus is filter, we are getting grants from European Union for border guard, so forgive them.