Visiting open National Gardens near Tetbury

We headed off to visit a private garden being opened for the afternoon as part of the National Gardens scheme. We don't often do these visits but it is fun to see other peoples' endeavours and hopefully be inspired. In the end we visited two wholly different gardens close to Westonbirt in Gloucestershire, the first being a converted dovecot originally built in 1499 and now a plush home with extensive gardens both formal and wild.  The second was the home of a couple who run a pottery  and where they had also organised for a range of artists to exhibit for the weekend.

It was very hot and we were rather slow in pottering about.  In the first garden which was less impressive there were the usual borders and pretty spring flowering plants.  I actually preferred watching the damsel flies flitting around the lilies and hostas around the pond before wandering into the small planted wood where there were several magnolia trees in flower.  But most interesting was the rare handkerchief tree which was also flowering. I have added a picture of one of its flowers as an 'Extra photo'.

At the second garden there was also a pond and just before we left I spotted another couple of damselflies both blue and red ones.  But then I noticed this huge insect flying around the reeds, which then landed on a lily stem.  I don't remember ever seeing one like this before so I have blipped it here, although it is heavily cropped. I don't know what it actually is, so any help in identifying it would be much appreciated.

EDIT:
Lathyrus has kindly told us it is a male broad-bodied chaser dragonfly.  Thank you very much. You can rely on the blip community!