The French-Thai Butchery has its main store at Sukhumvit Soi 33 (near Villa Market). Besides that it also has its counters at Villa Market all around Bangkok. The French-Thai Butchery supplies halal grade 1 beef. You have the choice to pick any parts of the beef which you like based on the chart provided. Unfortunately, they do not carry lamb.
Allowrie butter and cheese produced in Thailand are halal, but the ones imported from Australia are without the Halal certification. There are a few other brands with the Halal certification. There's even halal mozzarella cheese at Home Fresh Mart.
There's a Halal minimart called Halal Express at Minburi, on the way to Nong Chok.
Fresh beef and lamb cuts are available at Sindhorn Steak House minimart on Ramkhamhaeng Road.
Fresh beef, mutton and lamb are available in the morning at Silom Soi 20 Market & in front of Masjid Ban Oou, behind Robinson's Bang Rak.
Ramly burger and chicken sausage are available at Carrefour Rama IV and a Muslim shop adjacent to Fahana Italian Restaurant on Rama IX Road.
p.s.I shall keep updating this post with current info from time to time.