You can transfer a Class 1 medical from one EASA member state to another for a fee but cannot simply convert another medical from outside EASA-land into a UK EASA Class 1 medical.
You will need to undergo an initial EASA Class 1 medical INCLUDING the colour vision test, which is far more stringent than the FAA colour vision test.
You are permitted to make up to 6 errors on the Ishihara test in the USA. You are not allowed any errors in EASA land.
Following errors on the Ishihara test, you will have to take the CAD test, a computer based colour vision test taken in two stages, a short test and an extended test. If you pass the short test, all well and good, you get your Class 1 medical but any errors and you have to take the extended CAD test. If you pass this you are classified as 'Colour Safe' and you get your Class 1 medical but if you fail you will receive a Class 1 medical restricted to Daytime Flying Only and No Commercial Air Transport - this is a deviation from the EASA regulations which applies only in the UK; other EASA member states will not issue you with any Class 1 medical.
As for the rest, you require a current, valid type rating on an EASA multi-pilot aircraft, 1500 hours total time, 500 hours of which must be multi-crew with other criteria for night flying, IFR, cross country, etc.
You will also need to do the Radio Telephony examination for a UK issued licence and an ICAO Aviation English language test for any EASA member state.
The good news is that, provided you meet all the above criteria you are exempt mandatory training for the exams and you can self-certify to sit them; however, the majority of convertees sign up with a training provider such as Bristol Groundschool ( other training providers are available
) and attend the classroom sessions.
Hope that helps.