When travelling from the EU countries to the UK, you do not have to pay any tax or duty on goods you have bought in another EU country, as long as tax was included in the price when you purchased the items, the items are for your own personal  use, and have been transported to the UK by you.

Still, there are limitation on alcohol and tobacco products:

3200 cigarettes
400 cigarillos
200 cigars
3 kg of smoking tobacco
110 litres of beer
10 litres of spirits
90 litres of wine
20 litres of fortified wine e.g. port or sherry

From Estonia – 200 cigarettes or 250g of smoking tobacco
From Bulgaria, Hungary, Latvia, Lithuania, Poland, Romania and Slovakia – 200 cigarettes

Here are the limitations, when coming to the UK from outside the EU:

200 cigarettes, or 100 cigarillos, or 50 cigars, or 250g of tobacco
4 litres of still table wine
1 litre of spirits or strong liqueurs over 22% volume; or 2 litres of fortified wine, sparkling wine or other liqueurs
16 litres of beer
60cc/ml of perfume
£300 worth of all other goods including gifts and souvenirs