There are two types of halal meat, stunned and non-stunned.
You'd be hard-pressed to buy the non-stunned stuff from anywhere other than a specialist Halal butcher in a predominantly Muslim area.
In Tooting, South London, you can see butchers with 'Guaranteed non-stunned' signs up in their windows, to differentiate themselves from the places that sell stunned Halal meat which the fundamentalists devout don't consider 'proper' Halal. So boycott away, but I'd be amazed if you had ever bought any in the first place.
Then we have stunned Halal meat. This is what was at the centre of the storm in a teacup last year, when the press were churning out all the 'OMG your Subway/Burger King/KFC/Tesco meat is actually, secretly Halal'.
Here is why that story happened:
The vast majority of chickens are killed in meat processing plants. Chickens start in a pen and are hung feet-first onto a conveyor belt. The conveyor belt firstly goes over a big water bath which has an electric current run thought it. As the chickens heads hit the water, then are stunned.
The conveyor belt then takes them onto the slaughter room where they have their throats cut and bleed to death pretty instantly. Then they are plucked etc and you get chicken to make into sandwiches or put into plastic trays to sell in the supermarket.
Years ago, someone realised that if you have a loudspeaker playing the relevant holy words at the chickens while they have their throats cut, you are effectively producing Halal meat, which can obviously be sold to an even bigger market.
Of the chicken that is produced that day, some will be labeled Halal and sold on to places and people who specify it, the rest will be labeled as chicken.
Lamb is produced in a not-too-disimilar way, hence halal lamb is also widespread.
The real issue is not whether they are played some words through a stereo on the wall. It is whether chickens should be slaughtered this way at all.
So if you really care about animal welfare, buy organic, buy local and buy from producers who care about the life AND death the animals have had before they become your meal