Welcome to Flyertalk, badgerW!
(I'll refer to the UK below, as I know little about hotels in Ireland...)
What you may find when looking for places to stay in the UK is that chain hotels are less well represented than in the US, particularly outside business destinations. In fact, you may find, in some locations (but by no means all) that prices at some of the US-based chains are hugely inflated, thanks to many places attracting business travellers who don't really mind what rate they pay to stay at that chain.
Now, that isn't to say that it's all like that. A lot of the international chains have bought into the UK market by buying existing chains or properties. Outside the main cities, this often means small, edge-of-town type Holiday Inn Express or Courtyard by Marriott properties - generally pleasant enough.
Starwood and Hyatt are fairly poorly represented in the UK, although Starwood has a few places in London.
Hilton tend to run very business-orientated hotels, trading on the name. However, Doubletree are expanding here, and get a good name.
Marriott and Renaissance have a relatively sparse presence, although Courtyard seems to spread out along the motorways.
InterContinental group, I would guess, have the largest of the lot, particularly as Holiday Inn Express seem to be entering into the 'budget hotel' explosion along with the UK chains Travelodge (not the same as the US chain) and Premier Inn. A lot of Holiday Inns around too, of very variable quality, and a few Crowne Plazas, which tend to be more at the "Americans will pay extra for this" end.
Best Western here, is a bit of an odd one (actually, there was a very interesting 'back to the floor' style documentary on it recently). It's not an especially big brand, and does not operate any of its hotels - nor does it have any particular design standard. The hotels are fully independent, and Best Western is really just a group used to market them. As a result, the style and quality is hugely variable (and I'm not sure the 'élite benefits' will always translate particularly well).
Carlson do have a number of pleces - Radisson Blu hotels tend to be city- or airport-based, and Park Inn have gone for the take-over-and-refurbish approach, but have done this very well in some places (they've also taken over some nightmare ex-Swallow hotels).
One British chain worth a mention is Premier Inn. They're a budget hotel chain, but do it extremely well, with consistently high standards of comfort and service. Just don't expect your bags carried or free wi-fi.
Another small UK chain that I love, but which is rather more expensive, is Hotel du Vin. They always have interesting properties, and extremely comfy, homely, rooms.
The notion of élite status in hotels here isn't quite as widespread as in the US. Among Flyertalkers and regular travellers, sure, there may be some expectations, but this is the exception rather than the rule, in my experience. Outside of London, there isn't really the notion of a 'boutique hotel' - they're just 'hotels'!
Also, don't forget B&Bs - we have loads (and in Ireland, you'll get one of the best cooked breakfasts you'll ever experience...)
Not sure how helpful this is (or whether others will agree), but it's certainly how I see the situation here.