If you don't want an instrument rating it's Articles 9/10 you need to follow: (edited for PPL/SEP)
Article 9
Condition for conversion of licences2. The holder of the licence to be converted shall comply with the following minimum requirements for the relevant aircraft category:
(a) demonstrate knowledge of Air Law and Human Performance;
(b) pass the PPL (...) skill test, as relevant, in accordance with Annex I (Part-FCL) to Regulation (EU) No 1178/2011 (...);
(c) fulfil the requirements for the issue of the relevant class or type rating, in accordance with Subpart H;
(d) hold a medical certificate, as required and issued in accordance with Annex IV (Part-MED) to Regulation (EU) No 1178/2011;
(e) demonstrate language proficiency in accordance with FCL.055 of Annex I (Part-FCL) to Regulation (EU) No 1178/2011;
(f) have completed at least 100 hours of flight time as a pilot.Article 10
Conditions for acceptance of class and type ratingsA valid class or type rating contained in a licence issued by a third country may be inserted in a licence issued in accordance with Annex I (Part-FCL) to Regulation (EU) No 1178/2011, provided that the applicant:
(a) complies with the experience requirements and the prerequisites for the issue of the applicable type or class rating in accordance with Part-FCL;
(b) passes the relevant skill test for the issue of the applicable type or class rating in accordance with Part-FCL; 2.6.2020 EN Official Journal of the European Union L 170/5
(c) is in current flying practice;
(d) has no less than: (i) for aeroplane class ratings, 100 hours of flight experience as a pilot in that class; (...)
What this means in practice is, you go to a UK ATO and say you want to do an ICAO to UK PPL conversion.
You pass the 2 theory exams and do flight training as required. The ATO will issue you a Course Completion Certificate. http://publicapps.caa.co.uk/docs/33/CAA5016Issue03Enabled.pdf. This complies with the "taking account of any credit based on a recommendation from an ATO" phrase of Article 3(b) within CAP2024A000
Then pass a skills test with a UK examiner, he will issue you with a skills test report form SRG2128: SRG2128: Examiner Report for PPL(A) Skill Test (http://publicapps.caa.co.uk/modalapplication.aspx?catid=1&pagetype=65&appid=11&mode=detail&id=5196)
Because you'll be claiming credits based on your ICAO licence, it will have to be verified using form SRG2142, which is now an online service: https://apply.caa.co.uk/CAAPortal/servlet/SmartForm.html?formCode=TCV
Once you have it all, you can apply online for your UK PPL here: https://www.caa.co.uk/General-aviation/Pilot-licences/Applications/Licences/Online-application-forms/
Bear in mind that documents submitted to the UK CAA must be certified. They are very particular about this. Read what they say about this carefully: https://www.caa.co.uk/Commercial-industry/Pilot-licences/Applications/Documentation/How-to-get-copies-of-your-documents-certified/
If you're not sure about anything, give the CAA a call on +443300221972 (tel:+443300221972) and also send them an email so that you have written proof:
[email protected]
EDIT: Corrected to Article 9/10 for conversions.