. I am mostly German with some Scottish, Welsh, and flat out Brittish. My dad was 3/4 German, 1/4 Scottish and my mom was 1/4 Welsh, 1/4 Brittish, and 1/2 German.
Since Chavster is still apparently counting sheep, I'll just jump in and point out that "British" isn't a race any more than "American" is. British is an all-encompassing term for anyone of English, Scots, Welsh or Northern Irish origin, though most nationalists in Northern Ireland will object to the term. So I'm assuming your mom was probably 1/4 Welsh, 1/4 English and 1/2 German? 
That is what I meant, I always get the term "British" and "English" mixed up
It is confusing. England=English, Scotland=Scottish, Wales=Welsh. The whole island is Britain and all 3 can call themselves British if they like. Now Northern Ireland is a different deal. I personally feel that there is two islands, one named Ireland and one named Britain and the folks on the one island should be called British and the folks from the other island should be called Irish but maybe that's too simple.
Not too simple, but not accurate

Just like Mike ^^, you're confusing race and nationality

Politically, the people of England, Scotland, Wales, Northern Ireland, the Channel Islands, Isle of Man, Gibraltar and the Falkland Islands are British.
Racially and genetically, the people of Northern Ireland are Irish, in the same way that people in Cork or Dublin are Irish.
As X Man mentioned, 'British' isnt a race. English is a race, Scottish is a race, Irish is a race, and Welsh is a race, but British is an umbrella term for citizens of the UK, and that includes Northern Ireland. From a UK perspective, anyone born and raised in Belfast (for example) is referred to as an Irishman, but when it comes to matters of state, the same person is British.
There is also another native race within the UK, which is Cornish. Welsh and Cornish are the two most medieval races within the UK.
No country that has been 'produced' from an amalgamation of other countries or territories or races can be described as having its own race. Places like the UK, US, the former Yugoslavia, Russia (etc) dont have a defined race, and the same is said for countries which have experienced mass immigration, such as Australia, New Zealand, etc.
There are pockets of 'pureness' within each of these countries, obviously, such as French Canadian, however the term 'French Canadian' in reality is applied to Canadian people who speak French as their native language, rather than to their race, because pure 'French Canadians' are in fact racially and genetically French. The islands of St Pierre and Miquelon (just off the coast of Canada) are also purely French, in spite of living off the coast of North America. Many people living in a town in Argentina (I cant remember the name of the town) are purely Welsh, as their bloodline has never been mixed with either the Spanish population of Argentina or the native population.
The thing to remember is that race isnt defined by politics, its defined by DNA, which is why anyone with an Irish bloodline is Irish rather than Mongolian-Irish or Irish-Brazillian.