We do have one, the UK Space Agency
We have had a fair bit of involvement in space activities over the years. We even launched our own satellite, using our own rocket
Prospero (satellite) - the only satellite launched into orbit using a British rocket, in 1971, launched from Woomera in Australia.
This made the UK the sixth nation to launch a satellite using its own rockets, after Russia, the US, France, Japan and China. Timeline of first orbital launches by country
We sent a lander to Mars, as part of an ESA mission to Mars, and it is the only spacecraft so far to land on Mars not sent by the US or Russia. The ExoMars Schiaparelli lander on 19th October will be the second such lander, in an ESA / Russia collaboration.
Our Mars lander was almost successful. We now know that it landed successfully but one of its solar panels failed to unfurl.
Orbital photograph of Beagle 2 - Wikipedia on the Mars surface - shows that (probably) one of its solar panels failed to unfold, so blocking radio transmission back to Earth.
And right now Britain is actively engaged in developing the Skylon space plane.
The engine has passed its tests with flying colours, and the project is on course to lead to a plane able to fly directly to orbit some time in the 2020s with much lower cost to orbit than even reusable rockets.
We are also very involved in ESA activities, for instance British scientists were involved in instruments for the Philae lander on Rosetta.
There are plans to develop a spaceport in Scotland Spaceport Scotland | Home
Also Virgin Galactic which aims to achieve suborbital tourism is led by a British entrepreneur Richard Branson though based in California.
We could do a lot more if there was the political will. Our government recently chose to spend huge amounts on renewing the Trident nuclear missiles. It may well spend more on renewing Trident than the total cost for the ISS for the US, ESA, Russia and all the other partners combined.
We have the technology and expertise, also the ingenuity and inventiveness and a long history of explorers. It’s a matter of priorities and politics. It never seems to have been a huge priority for us but our role hasn’t been that small either.