On the MR side, nothing is as straightforward as you might imagine. Essentially all teams are charities and will fundraise to help with their own running costs. This is typically anywhere between £15k to 50k+ depending on the team's location and how busy they are. These costs won't include capital purchases like vehicles / HQ build etc.
Some teams are very lucky and have 'sugar daddies' in the local area who will support them (think Edale and their HQ at the cement works), other teams have to raise money to fund their HQs if they can't find a local backer.
The National Co-ordinating body for Mountain Rescue in England and Wales is MREW
link. If you donate to them the money will likely be used to fund courses that will benefit all MR teams in MREW, or to purchase items of equipment for all MR teams. If you just want to support MR on a national level, this is the best place for your money.
In the interests of completeness, Scotland is covered by
Scottish Mountain Rescue and Ireland by
Mountain Rescue IrelandIf you are Peak based for example (and other areas will be similar), there are 7 teams who operate throughout the Peak, covered under the umbrella organisation of the Peak District Mountain Rescue Organisation (PDMRO) -
link. Again, you can donate to the PDMRO in which case funds will be used to support training / equipment at a regional level, rather than a national level.
Finally, if you have a local team (or a team you have affinity with), make contact with them and they will be more than grateful for your donation. Any team should have the ability to allow you to setup a direct debit. Many teams have supporters networks which involve anything from monthly / quarterly newsletters or options to get more involved with the team if that's what interests you. Bear in mind that (again, using the peak as an example) depending on whether you're climbing at Stanage, Black Rocks, Stoney or Wimberry, each of these would be covered by a different team.
Hope that helps, but regardless of who you donate to
for supporting MR. I don't think a lot of people appreciate just how lucky we are in the UK!