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

Heathrow Airport
One of the largest airports in the world, and the largest in the UK. Serves as the primery hub for British airwayes, virgin atlanic and major hub for BMI. 

Location 24KM west of Central London

Transportation

Train Heathrow express – a non-stop service directly to London’s Paddington station; trains leave every 15 minutes for the 15-minute journey

Tube- London Underground Piccadilly line: four tube stations serve the airport – Terminals 1, 2, 3; Terminal 4; Terminal 5 and Hatton Cross. The standard journey time from the Heathrow Terminals 1, 2, 3 tube station to Central London is 40-50 minutes

 Shuttle – door-to-door London hotel shuttle bus service is operated by Dot2Dot from each terminal, and HotelHoppa buses connect each terminal with hotels in the Heathrow area

Buses - Heathrow Airport has one of the United Kingdom’s biggest bus stations, with many local bus services (Transport for London) to nearby London suburbs.

Taxi- Takes around 40 minutes and cost around 40 Pounds to go to Paddington station

Stansted Airport

1 terminal

Location: 48km (30 miles) northeast of London

Train- Stansted Express train,  to Liverpool Street station £15 one way

Taxi – around 54 Pounds takes

Bus – EasyBus

Gatwick Airport

Taxi – A journey to central London takes approximately 65 minutes and costs around £77 (plus £5 congestion charge if your destination is within the charging zone).

Train – Gatwick Express offers dedicated, high-speed travel between central London and Gatwick Airport. With a journey time of just 30 minutes between London Victoria and Gatwick (35 minutes on Sundays), there is no faster way between the heart of the city and the airport.

A standard single fare is £16.90 and a standard return is £28.80. For details of special offers and to pre-book tickets visit http://www.gatwickexpress.com/

Luton Airport

Transportation

Train – Regular rail services to central London take as little as 21 minutes with Midland Mainline and 25 minutes with First Capital Connect.

London City Airport