First Britain has actually launched its own satellite into space with its own rocket as well. Only did this once, here is a photo
It was launched in 1971 from Australia - making us the sixth country to launch its own satellite from its own home built rockets. Prospero (satellite)
Earlier than that, the British Interplanetary Society way back in the late 1930s was already designing spaceships. Including a lunar mission plan complete with lunar module!
And a space station
Also been very active in developing ideas for interstellar spacecraft with Project Daedalus
And also more recently, Mars Beagle - which sadly failed - as have 50% of landers to go to Mars (though NASA has achieved 7 out of 8 success rate) so is nothing to be too ashamed of:
and through the ESA also - as with rest of Europe - we are involved in the ExoMars program
which is the first spacecraft to go to Mars with the capability of detecting life there since Viking - and the first one with any chance of detecting it unambiguously (because they didn't realise quite how harsh and strange the surface was when they designed the life detection instruments for Viking).
It is searching mainly for past life - targeting areas that are optimal for the search for past life - but is searching for present day life as well.
Then if you include private companies, we have Virgin Galactic of course - sub orbital hops pioneer - the spacecraft design of course comes from a US aerospace engineer Burt Rutan
And also - we are pioneering the truly innovative Skylon - British through and through - designed by the British engineer Alan Bond
- a plane that can fly directly to orbit - and can "breath oxygen" in the atmosphere - yet fly as a rocket as well in space. It achieves this by novel technology that cools the incoming very hot air rapidly in a fraction of a second to way way below 0C.
The engine has been undergoing tests and works just fine. They hope to get it to a first test flight maybe in 2018 and perhaps it can fly to the ISS by 2022 though it is of course far too early to note down a confident timetable for it.