It is possible, but it involves a ferry for which a supplement is due. I travelled on Irish Ferries (which offers 30% discount for interrail pass holders) from Dublin to Holyhead (Wales) and from there to London by train (Transport for Wales + Avanti West Coast). As far as I know, that's the fastest route.

Ferry discount: https://www.interrail.eu/en/plan-your-trip/tips-and-tricks/trains-europe/ferries/irish-ferries

Check times for Holyhead to London trains on nationalrail.co.uk. Be aware of ongoing strikes in the UK, which might affect this journey.

Ferry Dublin - Holyhead and train from there is the only non-flight route that is worth looking at.

There are 2 ferry companies, both offer a 30% discount on their standard foot passenger fares for passholders.

Irish Ferries as above run 2 daily sailings (4 in summer) If booked online you have to pay full price then request the discount by e-mail

Stena Line run 4 all year round https://www.stenaline.ie you can add “EURAIL” as discount code in their online booking form.

The ferry terminals in Dublin are a good distance from the city in a large industrial area and I would not advise walking to them. A bus service timed for all ship departures runs from Georges Quay in the city centre beside the entrance to Tara Street rail station.

Details and times are here https://www.nolancoaches.ie/services/ferry-shuttle-bus/

It can be pre-booked or just pay on board with contactless credit/debit card.

The ferries on the route are all large and do not generally run close to full so spaces are almost always available right up to departure time, there is no need to have travel on this route booked far n advance.

A bus takes passengers from the ferry to the combined ferry terminal/rail station in Holyhead. There is a delay with this so you should expect at least 30 minutes after the arrival time before being able to board a train.

Due to the lack of train connections I would advise not using the evening departures (20.30 or 20.55) from Dublin, there are few facilities in Holyhead, particularly late at night, it isn’t somewhere to spend 5 hours if you can avoid it. The 02.15 departure is preferable if you want an overnight journey.

As above, be aware the ongoing disruptions to rail services in Britain, you would need to check within a month of travel.

IF you are not saving every cent/avos/penny you could also consider:

1.overnight ferry also used to do direct Dublin-Liverpool, giving more of a good night rest, but check if this still runs/on your dates

2.book yourself a seat on a coach (autobus) direct from Dub (Busaras=station) to some place in UK-saves all the hassle with changes at ports-might even be cheaper or same price as all the total cost even with the pass-discount. The reason why these ferries are now so far away is that for 99% they aim at people in cars and trucks-in the past they were very close to the train platforms.

3.OR if you would also like to see some part of Scotland-can go via Belfast/Ulster, then same type of bus+ferry combo on to Stranraer/Glasgow and onward. Not that many Mexicano can say they have been there!

More descriptions also as always on seat61.com

@mcadv please also check seat61 yourself. The ferry from Stranraer was relocated to Cairnryan a few years ago, with a bus connection from Ayr.

1 Dublin - Liverpool is not possible and hasn’t been since 2011 when Norfolkline-DFDS closed their route. The current operators only take cars and trucks, not foot passengers.

2 Only possible 2 nights per week (Thursday and Saturday) to Birmingham or London, https://www.expressway.ie/service-news/eurolines

More than a few years now, Stranraer ferry terminal closed in 2011 with the withdrawal of the high speed catamaran HSS service.