If I was to buy a DVD, bought in Australia (region4) would I be able to play it on a UK DVD player (region 2)?

Thank You

It depends. If the DVD was made by an entity trying to protect their market share, and therefor encoded as a region 4 disk, and your player is set to play only region 2, then it becomes more difficult. Some players can be set to be region free. Here in Australia, you can buy region free players, but you have to look for them, most are region locked.
Failing that, if you have a computer, you can "rip" the disk, and burn either a region 2 or a region 0 copy.
I don't know of too many DVDs being made in Australia, set to any region. My daughter sells dance training DVDs internationally, all burnt to be region 0 i.e. region free.
Regionalisation is against WTO rules, limiting free trade. Sony is responsible for the concept, and for forceing it on the consumer. As such, I do not buy any Sony product, nor do I accept regionalisation. Rip and Burn! If you bought the DVD, you are entitled to watch it, where ever you are.
Cheers, Ken