Quite a while since I was flYingc around in the UK , but I would suggest that East Midlands would give a suggestion of who to contact when you leave their airspace eg London Info. You will find the appropriate frequencies in the AIP & on nav. Charts.
I would also suggest that you are fully aware of which aerodromes & ATC units whose airspace you will fly through, or close to, during your flight. Again, these freqs. should be on Air nav charts, AIP etc. One word of particular advice that I would give you is to call appropriate Radar units eg Coventry en route. Having seen the problems ATC have at these units with light a/c flying through, or close to, their airspace it would help them enormously if you (& other a/c) worked their freqs. This also applies to military ATCUs. So, an appropriate one on your route would be Boscombe Down.
Once again, you should be able to check which units are involved on your nav. Map ( & the freqs.) or in the AIP (Air Pilot).
As an ex ATCO & PPL, I would always recommend using the appropriate ATC Units.