With united you can upgrade at the check-in desk for £70 per person (that was ~6months ago)... however the bad news is that you might not get seated together if upgrading like that - you probably would though.

However, to be able to choose different seats, and potentially pay for an upgrade, I believe the tip below works, but someone may correct me...
1 - Get your united booking reference from checkmytrip.com using the code that BMI gave you when you booked
2 - Call up United and ask for your ticket number (using this reference number).
3 - Using that ticket number you can then choose seats on the united flights using their website.

Not sure if it might also let you upgrade the tickets at the same time, but its a quick and easy way to find out.

I rather stupidly didn't do this on my (only) united flight - I thought, "OK, won't get the best seat in the plane but it won't be that bad if we don't prechoose seats" to find all the other BMIers on a code share were sat together at the back of the plane in the middle (and couldn't change seats even checking in 3 hours early).... won't make that mistake again! On the way back we were upgraded to Y+.... again sat in the middle. Slightly more legroom but otherwise identical service. I wasn't impressed and wouldn't fly united again (at least not in Y) but it did earn 1x miles!

PS You don't say whether you paid cash on a codeshare, or this is a reward flight?