The Britons are primarily an archer oriented civilization, with many of their civilization bonuses aiding their offensive capabilities.
Strengths
Their archers gain bonus range in the Castle and Imperial Age and are trained faster. In addition their unique technology increases their range even more and grants towers additional attack. In total their foot archers gain +3 range, giving them an advantage against the archers of other civilizations. Their unique unit, the Longbowman, has the longest range of any archer. Due to their range Longbowmen can cut down opposing forces before they can even get close. Even enemy archers will likely be killed before they get in range. If in a large enough group they are almost impossible to counter. Cavalry are the main threat of Longbowmen, but the Britons have full infantry technology so can build Halberdiers to provide close combat protection from cavalry for the Longbowmen. If played in conjunction with the Saracens, their team bonus will allow longbowmen to deal additional damage to buildings.
Weaknesses
However the Britons have several weaknesses. They have mediocre cavalry, lacking both the Hussar and Paladin upgrades and cannot build Camels. Their siege weapons are similarly lacking, missing the Siege Ram, Siege Onager, and Bombard Cannon. They are missing the Parthian Tactics and Thumb Ring upgrades, though their inherent archer bonuses compensates for this. They are also the only Old World civilization to be missing the Cannon Galleon. This is a critical weakness in maps where water is common as this causes naval invasions to be much more difficult. If an opponent builds a large amount of towers near a shore a naval attack is almost impossible.
Strategy
Britons should avoid Dark Age rushing (drushing) at all costs. It is critically important to frequently scout the base of the enemy to try to determine which strategy they are using. If you see a Barracks going up in the earlier half of the Dark Age, it is highly likely they will drush you. In the event of this, wall yourself in with palisades and buildings. It's all right to constrict your space, just try to keep the enemy out. Go up on 22 population, and get an Archery Range up as soon as possible. A few Archers should be more than enough to break the siege from behind your walls. Then, go out and harass your opponent with Archers.
If you don't get drushed, then you should still use essentially the same tactic. Go up on 22 population (21 villagers+a scout) and rush the opponent with Archers in the Feudal Age. Since Archers only take Wood and Gold, they shouldn't hinder your progress to the Castle age much, so long as you get a few extra Villagers on wood and gold. Britons can get out of the Dark Age faster than many other civilizations, since their Shepherds work faster. It is important to press this advantage by Feudal Age rushing (flushing) the foe with Archers as early as possible. Since Archers only take Wood and Gold, they shouldn't hinder your progress to the Castle age much, so long as you get a few extra Villagers on wood and gold. In the Castle Age, just upgrade the Archers who are ideally already raiding the opponent into Crossbowmen, and research as many relevant Blacksmith technologies as possible. Be sure to protect your Archers with Pikemen, as Knights can be hazardous otherwise.
You can optionally switch into Longbows in the Castle Age, but Crossbows and Arbalests are generally more effective, unless that extra one range is really important. Trebuchets make good Imperial Age back-up, as Britons lack proper Siege. Always keep Melee units on hand, as enemy units will often hide in rams to approach safely.
Britons tend to fare worse on water maps, as their navy is poor, lacking the Cannon Galleon. Typically either win the water early on and patrol the shores to try to keep towers from going up, or keep the boats away from the enemy and use them purely for defense.
Strategy changes in "The Forgotten"
Yeomen was moved from Imperial age to Castle age, allowing Britons to strike with archers heavily earlier than in The Conquerors (now with +2 range at Castle age and +3 range in Imperial age). New Tech Warwolf allows Trebuchet to do blast damage (damaging enemy buildings and units near to the firing point) so a combined force of archers, longbowmen and Trebuchets makes the Britons even better in a siege in this expansion. If played in conjunction with the Magyars, their longbowmen can have a range as high as 15 points, the highest of any unit in the game with the exception of several gunpowder and siege units. In addition, they have the ability to build Cannon Galleons making them an average naval force.