The initial BBC projections haven't always been right on, but their track record is pretty good overall:
2017 - projected Tories short by 12 (actually short by 8 )
2015 - projected Tories short by 10 (actually a majority of 12)
2010 - projected Tories short by 19 (correct)
2005 - projected a Labour majority of 66 (correct)
2001 - projected a Labour majority of c.160 (actually a majority of 167)
1997 - projected a Labour majority of c.175 (actually a majority of 179)
1992 - projected Tories short by 25 (actually a majority of 21)
1987 - projected a Tory majority of 26 (actually a majority of 102)
1983 - projected a Tory majority of 146 (actually a majority of 144)
(They didn't provide an exact figure in 1997 & 2001, giving just a rough estimate.)
They were rather off in 1987 & 1992, but otherwise were pretty close on all the rest (though you can debate if their 2015 exit poll was 'close' or not, I suppose).
1997 the BBC didn't broadcast the forecast but it was for a 209 LAbour majority and in 2001 they did broadcast seat numbers and the precise majority forecast was 157.I can give details of ITN if anyone likes and details for both channels prior to 1983