What little information I have, I should have said. Because it isn't a huge amount. One thing is certain: it was a regional style which was only found in a couple of areas of Britain.
Let's kick off with what Andrew Campbell had to say about Home Brewed:
"Between mild beers and stouts lie many types of brown ale, finished and filtered milds specially brewed for bottling. Brown ales again are sweet in flavour, but less full and creamy than stouts. Brown ales will probably be non-deposit beers to pour clear and sparkling, but stouts will often be left to work after bottling. 'Home-brewed' is a title often given to brown ales, and will be met especially in the West Country. An average gravity for brown ale is about 1033º, which is a little above the weakest milds. Stouts range from this figure upwards. Price is a good guide to gravity, for if the price of the stout should be a fraction above that of a brown ale then it may be taken that the stout is a fraction stronger. The gravity of a pale ale and a brown ale may be the same if the price is the same, but the odds are that the pale ale will be a little lower."
"The Book Of Beer" by Andrew Campbell, 1956, page 85.
After poring over all the information I have (it took a good 20 minutes), I've found confirmation that Home Brewed was produced in the Southwest. But I've identified a second region where it occurred: the East Midlands. It shouldn't come as any surprise to me. Because one of my favourite labels is a Warwick & Richardson Home Brewed.
These are breweries for whom I've found adverts or labels for Home Brewed. First those in the Southwest:
Gibbs Mew - Salisbury
Georges - Bristol
Bristol United - Bristol
Rogers - Bristol
Wadworth - Devizes
Starkey, Knight and Ford - Tiverton
Holt Brothers - Burnham, Somerset
Stroud Brewery - Stroud, Gloucestershire
Simonds, Tamar Brewery - Devonport
Charlton Brewery - Shepton Mallet
St. Anne's Well Brewery - Exeter
Devenish - Weymouth
Now those in the East Midlands:
John Hair - Melbourne, Derbyshire
Hoskins - Leicester
Warwick & Richardson - Newark
Home Brewery - Nottingham
And the one that doesn't fit the pattern:
Garne - Burford, Oxfordshire
Though I suppose Oxfordshire is bordering on the Southwest.
For those whose knowledge of English geography isn't great, here's a map to show you exactly where all those breweries were:
View Home Brewed in a larger map