Quite a bit down in Cornwall.
Probus - Burngullow was redoubled in 2004 - the one long stretch of single track on the main line. Long Rock - Penzance approaches, Pinnock and Largin viaducts, and the Royal Albert Bridge remain single, but all these stretches are short enough to have little impact on the timetable.
The Penryn loop was installed in 2008. Pedantically however, this wasn't a redoubling as such as the other platform wasn't brought into use, but more an efficient way of creating a loop to increase frequency without having to reinstate the old platform - a new solution to an old problem.
Not aware of any other Cornish redoublings, but then I think all of the surviving branch lines have always been single track anyway (not sure about Newquay given its historic freight traffic over the southern section).
This was the section Yeovil Junction to Sherborne, singled June 1967, reinstated to double track October 1967, thus making it likely the first double reinstatement. It was only possible in such short order because the previous second track had not yet been taken up.
Yes Sherborne - Yeovil Junction approach was reinstated in 1967 as the old track hadn't been removed. It wasn't possible to pass trains in Yeovil Junction station itself until 1975 however.
Tisbury loop was added in 1986 at a cost of around £500,000 at 1986 prices. Not sure what it would be now. Annoyingly it couldn't take in the station itself as the down platform had been sold off, so trains still have to pass each other with at least one at a standstill in a field in Wiltshire.
Axminster dynamic loop was created in 2009.
At the other end of Britain, Blair Atholl - Dalwhinnie was redoubled on the Highland Main Line in 1976. I think this was more for freight traffic labouring up to Druimuachdar Summit than anything else.