Hello and welcome from London.
The Series 1 4/4 is now becoming one of the most prized Morgans of them all , so I am sure you will be well rewarded by undertaking a a painstaking rebuild.
Firstly I would advise you to register your car's details (Chassis Number , Build date, Engine number) at The Morgan Registry http://www.morganville.org
Secondly Bill Hughes is an expert on these cars and would love to swop details of your car for some information billhughes at privauk.freeserve.co.uk or bill at morganseriesone.com
Thirdly the Club Series 1 technical advisor is George Proudfoot (Tel +44 (0) 1329 236217) There is not much he does not know about these cars as he is an active competitor in them for many years .
Fourthly there is Colin Bray who is currently completing a Series 1 restoration from the proverbial "box of bits" He is in Canada (Ontario?)I know that is hardly next door , but at least he is on the right side of the pond
Lastly there are several lurkers on this forum who will be able to help at different times, amongst whom is John Merton from Oz who asked me to post this for you:
The engine number, plus the bore diameter of the engine will be found stamped on the front of the block, just above the timing case. There will be an "M" with a gap to the engine number, then another gap to the bore size in mm. JP Pistons in Adelaide should be able to help with new pistons, although the size they generally supply is for the 1122cc engine. I suspect that owners of Triumphs with the G10 engine, from memory 1087cc, may be boring out to this size, at a rough guess about a 40thou overbore. I've a suspicion that the 1098cc engine used in a few Morgans may have been the 1122cc block underbored (Triumph made their own engines under a licensing arrangement and there were quite a few differences to the CC built product).
Also look at the Series 1 section of Morganatica https://sites.google.com/site/morganatica/engine/coventry-climax
And the Morgan Owners Club of Australia (MOCA) http://www.morganownersclub.com.au/The%20Coventry%20Climax%20IOE%20Engine.pdf
Please post lots of photos as you delve into the rebuild and we can all follow your progress and try to help