@Claudi. Can you please assist here?

We do have some guidelines available on this page in cases of dual citizenship, etc. In this case, it would be useful to mention that generally speaking: 

We do recommend entering the country where you currently permanently reside as your country of residence. If your country of residence is different from your citizenship, then please remember to bring your government-issued proof or residence or ID-card along on your trip. 

In your case, you are eligible to travel with either a Eurail or Interrail pass. With a Eurail pass, you will need to enter your Hong Kong identity card number and be able to show this card when asked for by a conductor. If you choose an Interrail pass, you can simply use your UK passport number and be able to provide this for inspection if asked for. Please remember to bear the in/outbound rules in mind when opting for Interrail. 

We do not have any real stats on how often ID documents are checked on train journeys. In theory, you should always be able to provide identification when asked for by railway or immigration officials. This is also our official advice. From personal and anecdotal experience this is not done routinely. One notable exception would be the Eurostar between the UK and Europe. I've also recently experienced vigorous documentation checks when traveling between Switzerland and Italy, so better safe than sorry :) 

Thanks for the information Claudi, I will go ahead with the HK id as the entered id for eurail.

I will be travelling on Eurostar, and also mostly in Switzerland, Germany and UK. If anyone else has any thoughts on frequency and strictness of checks on trains, that would be useful. As I said, I am not trying to cheat anything, I just don’t  fancy having a difficult time with passport / id etc every time I get on a train! And worst case, having some train staff not willing to accept. 

Myself-being NL and living here-so no issues-had a 10Din 2 M pass last srping and was not checked once for ID  in that time-travelled in 10 countries.

In a 2-month continue pass last autumn 2 times-once clearly by an apprentice conductor+instructor-delighted to show/explain some unusual ticket and we had a nice chat about it and travels etc.

Countries where people tell there are more checks as average: Swiss and GB. Some GB forums for railfans explicitly give advice for those tipical Brit railfans roving around a lot in their own country on how to have proof that one does not live in UK etc-also in GB there may even be checks if one uses the OUT/INbound days to show that one has a ticket (€*, ferry, plane) that one indeed goes to travel abroad. But that will not apply to you

@Claudi. This is a strange advice, so I'd like to have some clarification about that.

Identity cards are, as far as I know, only delivered by the authorities of the country of which you have the nationality. Any document from the country where you live, if you don't have the nationality of that country, will normally be a residence card, not an ID card. In some countries, a residence card may be accepted as an ID, but usually in that country only. That means it is normally impossible to enter an ID card number of the country where you are only a resident.

The number to enter on the Interrail/Eurail pass, however, should be a passport or identity card number. Are you now suggesting that people enter the number of their residence card?

The page you referred to also suggests to use the "passport/ID of the country you live in”, although this is not possible if you don't have the nationality of the country you live in. This page should IMO therefore be updated to clarify this point.

@rvdborgt I think you need to make a difference between an ID card and a national ID card (NID). A NID you only get for the country where you are a citizen but an ID card it is possible to get in a country where you live. In Sweden the driver's license is a valid ID card in all situations including travels to the other Nordic countries.

An ID card only proves that you are you, whereas a NID also shows your citizenship. 

There are lots of countries where it is not possible to get an ID card of any kind if you don't have the nationality of that country. For example, in Belgium, if you're not Belgian, you can only get a residency card but that is explicitly not an ID card; it is only valid together with your national ID card/passport. And while in some countries a drivers licence may be accepted as ID, this only works in those countries but not elsewhere. In addition, I doubt if you can use a drivers licence as the ID for Interrail/Eurail, which is the issue here.

I can tell than like in Italy if you live in Italy, but are not italian or from an EU/EEA country you get a resident permit card (that you need for traveling in EU/EEA together with the passport of your nationality) and also an italian ID card, that can be used only in Italy, not valid abroad. 

If you are from EU/EEA I think you do not need resident permit card, because you are allowed to live where you want in EU/EEA. There you should also not get an ID card, because the ID card of your nationality is enough.

We need to differentiate between governmental cross border requirements (eg Eurostar from Mainland to UK is a formal passport check - no ID cards permitted) and the possible inspection for the validity of your rail pass (I suspect virtually unheard of as it has no interest to an on-board or station ticket check).

I cannot believe that anybody with any form of residency ID for a country other than their citizen country, would ever be challenged about whether they had an IR or Eurail pass.

The only concern would be somebody resident and a citizen of country A, then claiming residence in country B so they could travel freely in country A. This is fraud but how on earth would you identify it?

I think you're missing the point.

An ID card (or passport) proves who you are.

A residency card/permit proves where you live.

However, a residency card is not an ID card and does not prove who you are.

Interral/Eurail are requesting that you use on the pass the number of an ID card from your country of residence, something that is often impossible to have if you don't have the nationality of the country you live in. That means the information on the website should be changed to match with reality. If the number of the residency card should be used, then the website should just say so.