"There is no history of reserve teams playing in the same league as first teams in the British Isles".
A statement most football fans in that area would intuitively agree with, and at the least similar in sentiment to ones not infrequently uttered in recent debates - but a completely untrue one for each league system.
Even leaving aside the fairly trivial but politically charged cases of both Irish league systems and the quality of the separate Welsh pyramid where it seems to be rarer, it is far from as true as one might think in England or Scotland either. It is more that the many cases are too far down the pyramid or too long ago (or both) for most non-historians of football to know about.
In England, reserve teams are still allowed in Step 6 or Step 7 of the National League System (provided they are at least two steps below the first team) and the more amateur a football league you look at - both in the sense of the AFA and in lower leagues connected with NLS divisions - the more it becomes the norm rather than the exception.
But that is not all. A fan of Ipswich Town when they first entered the Football League in 1938 would likely have been taken aback at the idea they had never played league matches against reserves - in their last season in the Southern League they had finished behind Plymouth Argyle II (promotion and relegation between leagues being an even rougher concept in those days than it can be in the lower leagues today, champions Guildford City did not go up either - and even Arsenal's infamous 1919 promotion pales compared to some arguably more legitimate cases) and they only finished 3 points ahead of future main rivals Norwich City's II team as well, who in fact won several interwar Southern League titles of their own. Their 1935 win would be the last outright in the competition by reserves however, and in 1960, Exeter City II would be the last reserves to play in the league, most leaving for the (formerly London) Combination - which had itself featured first teams pre-war.
Further north, in 1922, the Third Division North was formed with teams coming from the Central League (becoming all-reserve as a result), the Midland League (which would be won by reserves every year from 1931 through 1937 and again from 1950 through 1955, still featuring Grimsby's and Scunthorpe's just before the NPL was formed), the North Eastern (won once by Newcastle Reserves and frequently by Sunderland or Middlesbrough's until 1956), the Lancashire Combination (won solely by reserves in the 1890s, often by Everton's in the 1900s, again by Nelson's in 1926 and Accrington Stanley's in 1955 and its second division frequently also, in both pre-WW1 and post-WW2 incarnations), and the Birmingham Combination (won by Walsall reserves in 1928 and those of Birmingham City, Wolves, and Villa twice in the 1930s).
Besides those of the above leagues surviving and with first teams (clearly still the top Northern regional leagues) the Northern Premier League incorporated sides from the Yorkshire League, which had been won most often by Bradford Park Avenue reserves (back in the first team's glory days) and was last won by Wednesday's in 1951, as well as the Cheshire County League, last won by Tranmere's in 1938.
In Scotland, the East and South of Scotland leagues still have the odd reserve team (and did pre-Lowland League when they were considered one step below the SFL), whilst further back the mostly reserve-based interwar Scottish Alliance League made a point of always having at least one first team, and the Division C of the SFL in existence between 1946 and 1955 also had a mix of reserve and first teams.