When did the UK first have democracy?

It would depend on HOW you define democracy. Parliaments were gathered from the 13th century, but they were made up from, and elected by, the upper classes of English society; not very democratic.

A form of democracy evolved, rather than was created, and that took several centuries. In the middle of 17th century, we had a series of clashes between Parliament and the Crown where Charles I sought to weaken the growing authority of Parliament; eventually dissolving Parliament completely and ruling 'by divine right' until the Civil War removed him. We then had a period of a republic, where Parliament ruled under Oliver Cromwell as 'Lord Protector' - King in all but name.

After Cromwell's death, we returned to a monarchy with increasing Parliamentary powers, and ultimately the right to vote for Parliamentary elections was gradually extended to all subjects over the age of 18, as it is today.

As a footnote, the extension of voting rights to women was only 100 years ago, so if you were to be pedantic, you could argue that true democracy came to these shores then, when equal voting rights were given to over 50% of the population.