If their flight is BMI domestic or to Ireland then they have nothing to lose going through immigration in T3 and then walking over to T1 later. I normally do this, it works great. The tunnels to T1 are near the arrivals lounge anyways.

If it's international then they're going through immigration when they could stay airside and skip immigration. But it sounds like they have plenty of time so that's probably not a concern.

Are you also going to T1? In which case I agree with the other poster, guesting them into the T1 Star Alliance lounge would be the thing to do. You can do this in addition to the Arrivals lounge, though there's not a whole lot of point, they both have showers and the food in the *A lounge is better. The only reason to do both would be to get some variety as 10 hours in one place is a bit tough.

For a 10 hour layover they might consider going into London btw. Or doing a tour of Windsor Palace. Or if you have cash you could get a day-return to Oxford and take a walking tour of Oxford and have lunch there.