>>> Royal Mail, NHS, British Gas, will never contact you from a mobile number
Somebody had better tell all of the NHS services that call me from mobile numbers about that then! My GP's surgery often calls from a mobile number and the hospital pharmacy always calls me from a mobile number, as do several other departments at Ipswich Hospital and also callers about Covid vaccination appointments.
Some 07 numbers are premium rate ones, rather than mobile numbers, so it's always wise to be wary of calling them. However 07786 is a regular Vodafone number (or a number that's been transferred from Vodafone to another service provider, as my own 07786 number has been), so whatever scam is being tried here isn't one where people are tricked into paying for expensive calls.
However submitting meter readings to British Gas (or to any other energy provider) today is actually something that's being legitimately encouraged
https://www.nationalworld.com/lifestyle/money/martin-lewis-households-meter-reading-31-march-energy-price-cap-3631372
It seems though that the vast number of people trying to submit meter readings online today has knocked several company's servers offline. The websites of British Gas, EDF and Shell Energy (or, at least, their 'meter readings' sections), are among those that have crashed today.