Trips to the rest of Europe by bicycle

first of all is the ferry

so we start with the main operators and their policies and fares

https://www.irishferries.com/uk-en/to-britain-from-ireland/

https://www.stenaline.ie/ferries-to-britain

From Holyhead to London Euston it is easy to put your bike on the direct Virgin service, bike reservation required and not difficult

from there you can do the Eurostar which is not easy unless you have a folding bike

Other options are the Dutch Flyer overnight or day service from Harwich UK to Hoek van Holland  Netherlands, bicycles should be allowed

The regular Dover Calais ferry service is quite good for making the connection to the continent. Your sail rail ticket from Dublin can get you all the way to Dover via London, then you bike to the ferry port. From Euston station you have to just bike a couple minutes to Kings Cross St Pancras to take the direct train to Dover. Simple

advice from Mark at the great train website, www.seat61.com

https://www.seat61.com/bike-by-train.htm

some ideas:

https://www.bikecation.co.uk/