Either the Phaart Bleep Dual at £1.99
https://www.planetx.co.uk/i/q/LIPHBPDRL/phaart-bleep-dual-05-watt-led-rear-light
or the Phaart Booster at £2.99
https://www.planetx.co.uk/i/q/LIPHBSTRL/phaart-booster-05-watt-led-rear-light
Occasionally they are on a crazy offer for about 50p and 99p respectively but well worth the full price. (I have both.)
I'm a big fan of these lights - especially for the price.
The Bleep is a fair bit brighter than the Booster, but the booster is still bright. The Bleep may be too bright tbh - I worry about hurting motorists eyes.
On a booster, I've managed to get 1,800 miles out of a set of batteries on flash (and I'm sure it could've gone further). I know it's about 1,800 miles because I ran one for a good while and only changed the batteries when I changed my chain, which is every 1,800 miles. I have the lights on whenever the bike is moving - even during the day. I don't know for sure, but I would expect the bleep to be similar.
They seem well sealed - I've never noticed any water in one, but I've had two boosters fail due to problems with the switch, which looked a bit rusty - probably just a build up of moisture over time. Bleeps seem to last ages too - either will last thousands of mile, but note I use mudguards. I have no idea how long either would last when being doused on a bike without mudguards.
The brackets that come with them look rubbish to me, but I've never used one. I just zip tie them on to either the seat cluster or the seat post clamp through the clip on the back.
I've had couple of goes with rechargeable lights - they usually last about a week until the little rubber bung for the usb socket is left off after recharging and they get wet.