pains in the chest is an emrgency in thheUK, and there is not one doctor who would not see someone on the same day when it's an emergency... and if by chance they had a doctor who woulddn't see the.. then they can call and abulance to take them to the emrgency room at the hopsital... Ambulances are free here... and when calling a dctor the voice at the beginning of all doctors surgeries would tell them if the patien was suffering from chest pains to call 999....
The UK has huge problems with the NHS currently.. and waiting lists for a regulalr GP appt can be as long as 4 week... 3 months is a lie.. I'm sorry to say but that's nonsense.. for a start the GP surgery doesn't have availability appointments beyond 4 weeks, so no-one could have said the appt was available in 3 months.... so whoever told you that was absolutely pulling your leg..