Please Need Help - Tyre Choice

It sounds like you are looking for a comfort style tire, one that is capable of riding on trails, but also is designed to reduce rolling resistance when riding on pavement.

Is that correct?

If so, you can just get the same size as you currently have on your bike.

So you currently have 26 x 2" MTB tyres?
Are they knobbly?
London paris is bound to be all sealed road and this would make knobblies a pain.

If so then you could probably go down to a 26 x 1.5" or even a 26 x 1" slick tyre. They will be more comfortable for tarmac and faster too.
Continental make their dependable "Ultra-Gatorskin" in a 26 x 1 1/8" which should fit your wheels.

If this looks to be a bit narrow for your liking then a City Contact, Top Contact or Travel contact may work too. Another brand to try in this market is Hutchison.

If I sound biased towards Conti it is becasue they have a good website with all available tyre options and they are ubiquitous in europe/UK: conti-online.com

The narrower you go, the less rolling resistance you will have, but surprisingly the discomfort does not go up proportionally provided you avoid the bigger bumps. The tire can cushion small pavement ripples and roughness because there's less area for the bumps to push up on the bike.

A 1" mtb tire is as wide as a 25mm road tire which is considered a step wider from standard.

However, how wide are your rims? If they are too wide, you may get a lot of flats due to the bead unseating during a bump and pinching the innertube in the middle. 26X2.0 tires came on a lot of different types of rims.

Plus, the really narrow ones don't handle gravel or dirt roads well.