I have a shower that wants replacing with a bath. It's in a conversion and everything is in 15mm. The closest I can run the 22mm from is 3/5m from the boiler then it'll be a run of 12/15m in 22mm to the bath. Can I supply the bath with 22mm? If so where's best to start?

Is sounds to me like you have a 1/2" feed and a 3/4" opening in your bathtub valve. Unless the manufacturer specifies a dedicated 3/4" feed you will be just fine if you put a brass 3/4 X 1/2" reducing bushing in the valve. Good luck, Tom

Is sounds to me like you have a 1/2" feed and a 3/4" opening in your bathtub valve. Unless the manufacturer specifies a dedicated 3/4" feed you will be just fine if you put a brass 3/4 X 1/2" reducing bushing in the valve. Good luck, Tom
Sorry I didn't say the bath would be a new installation. I've only got 15mm pipe to the bathroom. Can I run 22mm off the 15mm to feed the bath?

Yes. The water will flow fine.

Yes. The water will flow fine.
Excellent. Is it better to run the 22mm from as close to the combi boiler as possible? Hot and cold?

Really doesn't make that much difference. The flow limitation is in the 15mm. There is more volume in the 22 but you will not see any difference.

Can I run 22mm off the 15mm to feed the bath? Yes you can but itg won't change the pressure or the volume. Why do you want to do this? Back to you. Tom

Yes you can but itg won't change the pressure or the volume. Why do you want to do this? Back to you.
In my bungalow there's a wet room designed for disabled use. I want to fit a bath where the shower is, there is only 15mm feeding the wet room. I want to make sure there isn't extra strain on the boiler. Also I'd like to know if it makes a difference going from 15 to 22.

No difference, it was plumbed with 15 originally and gave no problems.