How far are you prepared to travel to get to/from the coach pick-up point?
National Holidays operate from the the northwest of England but there nearest pick-up point is Altrincham Coach Station, about 37 miles away from you. (They also pick up from opposite the National Express Coach Station in Manchester if that would be any easier for you).
The reason that I thought of National Holidays is that I've met many of their customers and never come across anyone who was disappointed. (The age profile of those customers is definitely very much at the 'mature' end of the scale, so they're well used to having elderly passengers on board).
In particular I was carrying out a footpath survey in Folkestone, just down the road from where hundreds of people were staying with National Holidays at a big hotel (where I stayed myself for one night, and was very impressed by the standard). Lots of people who were out for a walk passed my way and I got talking to many of them; they all had nothing but praise for National Holidays and the value their holidays offered.
For example, an elderly gentleman from Preston told me that he was on a 4-day/3-night break, with meals included, free entertainment in the hotel each evening, a day trip to Canterbury and another one to Belgium (Bruges), all for £99!
So if you can get to/from Altricham (or Manchester), National Holidays are definitely worth a look.
Current offers from Altricncham are here:
http://www.nationalholidays.com/your-holiday-search-results?min=2014-05-13&max=2014-07-06&t3p=1172
To find firms with more local departures, ask for their brochures at the tourist information offices in Liverpool and/or Chester.