As has already been indicated, left luggage facilities at most stations were withdrawn many years ago due to the threat of terrorism. However they still exist at major stations where there are independent companies (rather than rail firms) operating in accordance with security guidelines (which basically means that they must have X-ray scanners, similar to those at airports).
The relevant company at Paddington is the Excess Baggage Company (a.k.a Left-Baggage.co.uk), which operates across Europe, including at Heathrow, Gatwick and Stansted airports. Their charges are in line with the high prices that one might expect to pay at major airports too!
As Barry says, they're adjacent to Platform 12 at Paddington, just beyond the loos:
https://i.postimg.cc/CKTLq6xp/Paddington-LL.jpg
You can beat the queues by booking online in advance:
https://www.left-baggage.co.uk/en
Some hotels might allow you leave luggage but they'll probably be going against the advice of the Metropolitan Police if they do so.