bus transit in uk

Ok tks, but i have 1 wuestion, this train from birmingham to london operate by lner? Or other train also accept eursil pass?

LNER doesn’t operate that route. It’s operated by two companies: Avanti and London Northwestern Railway. 

You can use your Eurail pass. You don’t need a seat reservation.

A Eurostar reservation London-Paris is €30 in 2nd class. Eurail have a €2 booking fee on top of that.

Also see:

https://www.seat61.com/interrail-and-eurail-reservations.htm

You may want to have a quick look at a map of London railway stations.

Birmingham to London → will arrive in London Euston station.

London to Paris → will depart from London St Pancras International and arrive in Paris Nord.

London Euston is ~10 minutes walk from St Pancras International.  Unless it is raining really badly, by far the easiest route between the 2 is to just walk down the road.  It’s a single road and you cannot miss either station.

St Pancras International station is right next door to Kings Cross.  You should not enter “Kings Cross to Paris”, you should enter “St Pancras International to Paris” - this will result in a direct connection between the 2 cities.

*IF* your actual route is Birmingham to Paris, then the legs will be -

1. Birmingham to London Euston - direct train, no changes required
2. Walk from Euston to St Pancras International - 10 minutes, grab a coffee on the way
3. St Pancras International to Paris Nord- direct train, reservation required, costs €32

2 trains, 1 short walk.