Don't really want to pay Central London prices, but would like somewhere quite nice for a night away together. We are coming from Birmingham, so West/NW would be better, and on a tube line from Leicester Square / Embankment / Charing Cross would be good.
Book rail travel to London asap for the best price.
It's not for everyone, but I like to leave hotel booking until a day or two before travel and using Lastminute. com or Latebooking.com or Secret hotels, Trivago Lastminute deals, etc etc.,to find good rates in normally more expensive hotels.
Decide in advance if you want breakfast included in room price, it can often be bought at a nearby cafe at less expense.
Be prepared to spend some time online searching for a reasonably priced stay, .
If you really can't be bothered searching, try the Imperial chain, Imperialhotels.co.uk they have six hotels offering a range of quality and prices, better to book asap.
See the London underground website
https://visitorshop.tfl.gov.uk/ and select the best buy for you regarding travel tickets within London.
As others have said, Premier Inn, Travel Lodge are a bit clinical but not so expensive if booked in advance.