Forza Horizon

To see which cars are British Cars, go into the Autoshow and start looking. The medals are the same basic concepts for every car.

This list contains all British manufacturers that come on disc Source:

Ascari - 1
Aston Martin - 4 (2 are Barn Finds)
Bentley - 1
Eagle - 1
Jaguar - 3 (1 Barn Find)
Land Rover - 1
Lotus - 3
McLaren - 2
Noble - 1
Radical - 1
TVR - 1

These are not all unlocked at the start of the game. You must progress through the story to unlock enough cars without downloading any.

Downloadable British Manufacturers:

Aston Martin - 3 (1 in December IGN Pack, 1 in April TopGear Pack, 1 Pre-Order Pack)
Bowler - 1 (April TopGear Pack)
Lotus - 2 (1 in January Recaro Pack, 1 Unicorn (Play with developers, no longer available))
McLaren - 1 (December IGN Pack)
Ultima - 1 (Free Download!)

With the free Ultima downloadable car, you can grab this achievement for free. Be aware that it costs over 15,000,000 credits to unlock by yourself.

It is not possible to unlock medals using cars from a Car Club garage. You can only use cars available in your personal garage.

From HolyHa1fDead - "Or you could just view the complete list of cars that you need from the 1000 Club menu - it even marks the ones that are DLC."

You need to earn at least one medal in 20 different British cars. Press up on the D-pad to see the requirements for the medals.

Beware, although some cars are free to download, they still need to be purchased in game with either in-game credits or real money (MS Points), but that is the case for every car.

Unicorn cars
I do not include "unicorn" cars as free as you need to earn them and they are extremely rare, so most gamers will not have access to them.

Barn discovery cars
Barn discovery cars are available in the main game, but you have to progress through the story and multiplayer, to have them appearing on your map. Then you have to find them in the barn (wrecked). You have to wait until they are fixed before you can use them. There are 9 Barn discovery cars.
* 1964 Aston Martin DB5
* 1958 Aston Martin DBR1
* 1981 BMW M1
* 1992 Bugatti EB110 SS
* 1957 Ferrari 250 Testa Rossa
* 1956 Jaguar D-Type
* 1954 Mercedes 300SL Gullwing Coupe
* 1971 Plymouth Cuda 426 HEMI
* 1965 Shelby Cobra Daytona Coupe

Loyalty cars
To get your loyalty cars you need at least a save file from either FM3 or FM4. Depending on your level, you get those cars:
* 2011 MINI Cooper S (Level 1)
* 2011 Citroen DS3 Racing (Level 5)
* 2012 Dodge Charger SRT8 (Level 10)
* 1969 Chevrolet Camaro SS (Level 15)
* 2008 BMW M3 E92 (Level 20)
* 2012 Jaguar XKR-S (Level 30)
* 2009 Gumpert Apollo S (Level 40)
* 2012 Lamborghini Aventador LP700-4 (Level 50)

Forza Rewards Program
https://rewards.forzamotorsport.net/
Depending on your tier, you get rewards monthly. Redeem them on the site and they will be deliverer in your game within 4 hours. The rewards can be money, cars, tokens,...

Available DLC Packs
* October Car Pack (1957 Chevrolet Bel Air - FREE)
* November Bondurant Car pack (2012 Jeep Wrangler Rubicon - FREE)
* Season pass (2006 Lamborghini Miura Concepts - FREE)
* December IGN Car Pack (1971 AMC Javelin AMX - FREE)
* Rally expansion pack NOT FREE - NO FREE CARS
* January Recaro Car Pack (1995 Ford Mustang Cobra R - FREE)
* Honda Challenge Car Pack - FREE pack, includes 3 free Honda Cars (2013 Civic Si Coupe - 1986 Honda Civic Si - 2013 Honda HDP Fit - FREE)
* February Jalopnik Car Pack (1966 Ford Country Squire - FREE)
* March Meguiar's Car Pack (1998 Nissan R390 - FREE)
* April TopGear Car Pack (2002 BMW M3 GTR - FREE)

Complete List
* 1956 Jaguar D-Type (Barn discovery - main game)
* 1958 Aston Martin DBR1 (Barn discovery - main game)
* 1961 Jaguar E-Type (main game)
* 1964 Aston Martin DB5 (Barn discovery - main game)
* 1993 McLaren F1 (DLC)
* 1997 McLaren F1 GT (main game)
* 2005 TVR Sagaris (main game)
* 2006 Lotus Exige Cup 240 (main game)
* 2008 Aston Martin DBS (DLC)
* 2009 Lotus 2-Eleven (main game)
* 2010 Aston Martin One-77 (main game)
* 2011 Aston Martin V12 Zagato (Villa d'Este) (main game)
* 2010 Noble M600 (main game)
* 2011 Lotus Evora S (main game)
* 2011 Radical SR8 RX (main game)
* 2011 McLaren MP4-12C (main game)
* 2012 Jaguar XKR-S (Loyalty car)
* 2012 Bentley Continental GT (main game)
* 2012 Ultima GTR (main game)
* 2012 Ascari KZ1R (main game)
* 2012 Aston Martin Vanquish (DLC)
* 2012 Lotus Exige S (DLC)
* 2012 Bowler EXR-S (DLC)
* 2012 Aston Martin Virage (DLC)
* 2012 Eagle Speedster (main game)
* 2012 Land Rover Range Rover Supercharged (main game)

Summary: 16 cars (main game) + 3 Barn discovery (main game) + 6 cars (non free DLC) + 1 Loyalty car