Why don't you just get some quotes? There are professionals who spend all their working lives estmating the costs of a charter
The BHAB Handbook as all the main operators in it.
I suggest you start with those outfits that will need to fly least to do the job (i.e. close to Battersea)
If you have a fixed date or dates, don't forget to point this out, as prices vary depending upon the demand.