Brexit, UK Registration, Sailing in EU

[whacker]

Hi All

I am seeking advice regarding my current UK Registration....I do hope someone can offer some advice from experience.

I am an Irish citizen and resident and therefore I am within the EU.
I purchased my boat from a Maltese company and I have a valid Malta VAT PAID certificate dated Nov 2015.
My boat is registered on the UK Ship Register.
My boat is currently in Greece and the intention is for it to remain within EU/Med sailing waters.

Q1. Is my UK Reg likely to cause me any problems with officialdom whenever I have to produce documents within the EU?
Q2. If NO to Q1, is there any other valid reason why I should change my country of registration?
Q3. If YES to either Q1 or Q2, can anyone recommend an alternative EU country for registration that is easy, uncomplicated and cheap?

Many thanks in advance for all good advice.