Depends really where you’re headed and whether you’re after something for the whole day/weekend or something shorter term.
The Royal National Theatre car park on the South bank SE1 9PX is £8 per day and about the best price for the location, but if the location isn’t convenient the utility is lessened.
I’ve had limited luck with Westminster street parking (it can get stressful depending on what you’re doing/who you have with you, particularly around Covent Garden there are loads of closed roads and parking suspensions due to outdoor seating).
The other night I needed to drop off / pick up something from our office and I wound up at Source London for the 40mins I needed; cost wise it’s pricey but after I’d driven round for a half hour trying to find any vacant on-street spot I went for convenience over £
Edit: just saw you mentioned Bloomsbury so the Nat Theatre probably isn’t ideal for you