You'll have plenty of time. Security doesn't take long and I'm sure their main objective is to get you out shopping as quickly as possible!
There are public showers on the departure concourse, near the toilets. I would highly recommend getting one if you can as it will make you feel slightly more human on arrival at Heathrow! Note that there are no towels provided so bring a travel towel! If there is a long queue walk a little further down the concourse and you may find a shower with no queue!
Also worth noting is that you will likely be screened AGAIN when you go back to the gate and any liquids you've bought in the airport likely confiscated, so don't buy a huge drink!
There are toilets and drinking fountains in the gate area.