Old Tom is a sweeter style of gin that's been resurrected over the last decade, initially it seems at the request of london's mixologists who wanted this historic style back so that they could recreate classic Jerry Thomas era cocktails.
The (abbreviated) story of Old Tom takes us right back to the 18th century gin craze. Distillation techniques were crude, and gin which wouldn't have been very good quality to begin with was commonly adulterated with turpentine (one way to get that juniper forward flavour, but not the one you want) and sulphuric acid. To make it something like palatable it was also common to add quite a lot of sugar. Over the years distillation and quality improved but the taste for sweet gin remained.
Why its called Old Tom is subject to speculation (it's worth reading what Gin Foundry have to say on the subject) but it's a style that seems to have remained popular through the golden age of cocktails, and up until the Second World War when an increasing preference for dryer drinks pushed it out of favour. By the 70's it had all but disappeared, and then Hayman's resurrected it (and good on them for doing so). These days there are a few around, but Hayman's, as well as being excellent, is the easiest to find (Waitrose sells it amongst others) .
It's a noticeably sweeter style than London gin, and whilst the usual citrus and juniper elements are there it's the sweetness provided by the sugar and liquorice that really come through. I'm sometimes asked for a sweet gin so I'm glad to have this to sell (Hayman's also do a gin liqueur which is worth investigating too, it has a lot more sugar and is great for playing around with cocktails) but I think it's fair to say that it doesn't really shine in a G&T - it's not bad, but I prefer something dryer.
Put it in a Tom Collins on the other hand and it's a different story. In a drink that's going to be sweetened anyway the softer, rounder, notes of Old Tom are perfect. Indeed, I'd use it for any gin cocktail that has any kind of sweetness to it, or where you feel a bit of sweetness might be wanted.
The book to have if you have a bottle of Old Tom to play with is 'How to Mix Drinks or The Bon Vivant's Companion' by Jerry Thomas. Jerry Thomas was a New York icon and cocktail pioneer who toured America and Europe spreading the word about his creations with some impressive showmanship thrown in for good measure. 'How to Mix Drinks' is a seminal work, and whilst the instructions do seem to err on the side of brevity, and the quantities mentioned are often on an epic scale, it's an interesting book to browse through - especially if you want to know what people drank in the 1860's (I do, I really do). Hesperus reissued it a few years ago with charming illustrations - that's the copy I have - and it has plenty of useful suggestions for Old Tom...