Guess this as good a place as any but one show to look out for is Broadchurch. It's just finished here and has widely been seen as ITV's best drama in a number of years, probably this century actually.
Now it's a difficult one for you to research as I'd strongly recommend you don't google it as avoiding spoilers is key, but it basically focuses on the case of a murdered 11 year old boy and the unfolding investigation over the eight episodes, with the killer revealed in the final episode. Obviously if you can it's better to watch without knowing the killer - it really is a show that has captivated the UK over the last couple of months and genuinely got people talking and with so many UK murder mystery shows resolved in a couple of hours or across a three parter it's been a real treat to see this be allowed to play out over eight weeks.