Lori, of the tours you are considering, I've done both Best of Ireland and Best of England. I had the single supplement for both of them -have always gotten the single supplement.
Best of Ireland - Dublin nights (beginning and end at that time) were in the Harding Hotel. I was there 2 nights ahead and think I had a room with a double bed. Kinsale, the room was across the entrance driveway in a separate building and was huge, double bed (maybe queen?), big bath. Dingle - Castlewood House and Oh My Word! This was one of the best rooms I've ever had. Double room. Shower and separate tub. Long counter in bathroom. Breakfast was amazing as well. Galway - yuck. It was like staying in the house of an elderly maiden aunt. Pillow was flat as a pancake. It was clean but that was about it. This was probably the lodging I have liked the least on any RS tour. Westport - only one night, barely remember it. Portrush - no real memory of this one either so it must have been OK. Our tour returned to Dublin for the final night. Harding was fine.
Best of England - Bath - Brooks House - was a smaller room but mine opened out onto a little garden. It was the single bed type room but it didn't bother me. I stayed there for 2 nights prior to the tour and the tour has 3 nights to start there. Stow-on-the-Wold - Old Stocks Inn which was really nice. Double bed, nice bathroom, fridge. Lovely and charming. Conwy - The Castle Hotel - double bed, large room. Don't remember the bathroom which means it was ok Keswick - The Crow Park. Very small room here. Single bed. My guide gave me a choice of room with a bathtub/no shower but a view OR a room with a shower and no view. I took the shower, then felt bad when I realized the bus driver had to have the room I didn't want. He was really tall and I can't imagine him in that tub! This was OK for 2 nights. I apologized to the bus driver, who I really liked and he just laughed. Said it didn't bother him, he often had that room and it was fine. The people at the hotel breakfast were so nice - it was clear they really liked the guide and driver duo and took great delight in teasing them. Very fun. York - The Churchill Hotel - again very nice. Double bed. My room was across the street from the rail line but the windows must have had triple glazing because it did not keep me awake. London - The Fielding - back to a single bed, OK size bathroom and shower. The other solo traveler had a large room with a double bed but then she stayed one extra night and they downsized her to a room like mine. This hotel did not have breakfast so on the RS days we were taken to a cafe nearby. I stayed here an extra 2 nights and just went around to the Starbucks or as the guide called it St. Arbucks - to worship at the feet of the blessed mermaid.
I've done 8 RS tours (all single supplement) and I find there are some hotels I like better, some not as much. They are all clean and well-located and except for the B&B in Galway, I would stay at all the tour hotels again. I generally expect smaller rooms in cities and larger rooms in small towns or villages. On the GAS tour in Muerren which is a pretty small village, I did have a small room with a single bed but I looked out on the Almendhubel and the Shilthorn which was just jaw-dropping. Again on the GAS tour in very small Hallstatt I had a huge room! I have also done 3 tours that were in Italy or had a few nights in Italy and I did not find that I necessarily had better lodging further south.
I love the Best of England tour, particularly the guide, the itinerary everything. Best of Ireland just did not click with me but I am in a minority with that opinion.
I would pick which area you want to see first and then go for it.