First, I think it would take a small book to answer your question comprehensively, and second, you are confusing two distinct sets of trials. I will do my best to provide a brief answer.
The British recognised that the rimmed .303 round would need replacing from an early stage but world events conspired against this both in 1914 and 1939. About mid WW2 the General Staff decreed that Britains future infantry cartridge would be the .30-06, but by 1944 this had changed and it was to be the 7.92 x 57. Quite a lot of work was done on future weapon systems including the design and manufacture of the 7.92 SLEM self loading rifle.
The advent of the 7.92 x 33 Kurz changed all that and immediately post war an investigation was held to determine from basics what the new round should be. This was called “The Small Arms Calibre Panel” and was chaired by Dr. Beeching (of later British Rail fame) and worked out of the Armament Design Department at Fort Halstead in Sevenoaks. They examined several calibres in a variety of bullet weights. These were 6.5mm (using KJ cases), .30-06, 7.92
It reported in March 1947 with a recommendation that the calibre should be .27", but if tungsten cores were permitted the calibre could be reduced to .25". At the same time, the design teams at Cheshunt were working on the EM1, EM2 and other experimental rifles.
Two rounds were to be developed, the .270 and the .280, although both were actually .276 (7mm) calibre. The .270 did not last long and was only made in small quantities in late 1947 and possibly early 1948.
The 280 continued in the EM2 and other weapons and, being aware that this was a candidate for the new NATO cartridge, the extractor groove was modified to that of the .30-06 and the round became the .280/30.
I will not go into the details of the politics but the round was unacceptable to the US and so the .280/30 was developed futher. First was the .280 1st Optimum which was the same round with a Belgian bullet seated slightly less deep to allow a increase in charge weight. When it became apparent that this was not enough the case was extended to 49.5mm and became the 7mm 2nd Optimum. This was followed by a case redesign to produce the 7mmHigh Velocity with the same case length, This was tested against the T65 round in the US. Finally in an attempt to produce a round acceptable to the US the T65 case was necked to 7mm and became the 7mm Compromise.
As all this development work was done with the Belgians and Canadians the various 7mm rounds were tested in 1950 in Canada at the BBC Trials (Britain-Belgium-Canada) and Britain took the decision to re-arm with the .280/30 case with the belgian S11 bullet as the “Cartridge SA 7mm Mark I”.
This decision annoyed the US and when the Tories under Churchill won the next General Election he rescinded the decision and we adopted the 7.62 NATO round.
L. to R.
.280 aluminium case
7mm 1st Optimum
7mm 2nd Optimum
7.62 British made T65
I have a .270 but it was not in the picture.
Skip forward to 1969 and again the question of a new calibre was raised. This time a 6.25mm calibre was chosen and ammunition was made using .280/30 cases necked to 6.25mm. This was only a ballistic vehicle and bullet weight between 90 and 105grns were tested. The actual round was to be a longer thinner case, but only turned brass mock-ups were ever made. The round looked remarkably like the later US 6mm SAW amd some say this was a crib from the British work. This was done at the Development Lab at RSAF Enfield. but nothing ever came of it.
Left 7mm Mark I, right 6.25mm
In the late 1970s a trial was to be held for a new NATO round, eventually won by the modified 5.56mm. Britains entry was to be a 5mm round originally based on a necked down M193 case. It was found the bullet needed to be lengthened and this necessitated lengthening the case neck and it became the 4.85mm which was the round actually entered in the NATO trials at the Cold Meese development centre in the UK. A lot of work was done on the 4.85mm and it was made in ball, tracer, AP, blank, grenade and dummy loads.
Left to r.
5.56 British M193 type
4.85mm mock-up using 5mm case with additional brass collar
Various 4.85mm including grenade blank and short range.
Various 4.85mm traing blanks.
That is about it I think, but one day I intend to write the book!