If you meet the standards for medical declaration, ask the CAA for a National licence (UK PPL A). This will cost you £30. They don't have a bespoke form for it, they often ask you to fill in bits of other forms so that they can capture your details. They issued mine based on an email request. Having directed many flying friends to this service, you will get best results if you use the counter service. This will cost you money, but your time appears to be short!
With a UK PPL and a self declaration, you can continue to fly EASA aircraft until April within the UK and Permit to Fly aircraft indefintely.
You'll be able to log hours until you resolve your medical issues.