Yes, you will have to:
- have the required paperwork to enter the US (US passport or green card or visa or ESTA)
- Go through passport control
- Reclaim your checked luggage
- Go through customs
- Drop your bags just after customs. They will already have tags to your final destination so it takes seconds, no queuing at check-in or anything like that
- Go through security
A few years ago thinking one could do it in less than 2 hours would have been madness, especially for a non US citizen/PR.
Apparently the process has much improved recently and airports and airlines now think that this doable and sell such connections (though I have personally no experience with this).
Note that given the hassle for them if you miss the connection, airlines usually only sell connections they think have a good chance of being done in time.
If you miss your connection they will have to reroute you and possibly provide a hotel, pay for meals, etc. Remember that (in this direction) you are covered by the UK equivalent of EC261. You shouldn’t be out of pocket but you could face a signifiant delay. It’s a good idea to know alternative flights / routings in case you may need them, it might speed up the rerouting process.
Make sure you have all you need in your carry-on for a longer-than-expected trip (especially medication, but possibly whatever you need to spend the night if it comes to that).