There's always been some dispute about who was where and in what numbers, especially on the Rebel side. Here's the British orbat; there was no official brigade structure on the day, but :-
1st Wave – Howe & Pigott
Light Battalion (10 companies)
Grenadier Battalion (10 companies)
5th Foot, 38th Foot
43rd Foot, 52nd Foot
47th Foot, 1st Marines
Artillery: 6-pdrs, 12-pdrs, 5.5" howitzers
(Grenadier Coy, 35th Foot + all regimental pioneers detailed to act as "labour" for the RA)
2nd Wave – Clinton
2nd Marines, 63rd Foot
Mini Flank Battalion (five companies – 2 Grenadier, 3 Light)
Flank companies tended to be kept at full strength by drawing men from the centre companies; the latter were consequently weaker than expected (especially as each British regiment left a "camp guard" of 20+ men behind to protect their baggage). Each of the line battalions was thus at around 240 all ranks.
You can get a rough assessment of the Rebel forces from this map; it's not known for sure which regiments were present, especially the Massachusetts units, or in what numbers, but I think this is as close as you are ever likely to get without the benefit of time travel:-
link
Also, bear in mind that Massachusetts units were actually not numbered until 1778/79; prior to that, they were officially known by the name of their Colonel. This may inhibit tracing some of the units listed on the map.
It's worth bearing in mind that the traditional criticisms of the British plan overlook several factors – principally, but not exclusively, that
1) the tide was ebbing which made rowing fully laden boats harder, as did the heat;
2) there were only enough boats to take half of the 1st Wave in one go;
3) the north side of the peninsula (the Mystic River) could not be used by Royal Navy vessels as it had never been "sounded" by the Royal Navy because, quite simply, it didn't go anywhere;
4) it was not possible to take horses across, so the guns had to be manhandled and staff officers/commanders had to operate on foot;
5) the idea of landing on the Neck and cutting the Rebel forces in two is idiotic – it would have taken longer to get there (and back to collect the rest of the 1st Wave), no guns could have been landed there because of the mill pond (and the troops would have had to be landed either side of the Neck, not on it, for the same reason), and any troops would have had to defend themselves from two directions against overwhelming numbers.