Josieann
I'm going to comment that for some owners these homes away are actually what they regard as their favourite main family homes. Their London dwellings are just a pied à terre and they wouldn't live in them if it weren't for work and the kids' schooling. I think it will need more than an increase in council tax to stop the influx.
If they spend a significant portion of the year there, use all the local facilities - the library, the drs surgery, the post office, the shops etc, support local clubs and organisations and have a genuine connection to the area that's one thing.
If the drive down for a couple of weeks in the Summer and the odd bank Holiday with a boot full of groceries and otherwise leave the house empty or rented out during the Summer months to tourists then they are killing the local economy, massively reducing the need for facilities that permanent residents must now do without all year around and creating soulless bleak towns and villages that were once thriving communities.