In terms of packaging your options are :
Firkin - 9 imperial gallon cask = 72 imperial pints (minus wastage) = 40.9 litres, a bit higher than your knee - the standard cask size these days, if you ask for a "cask" that's what you will get.
Kilderkin - 18 imperial gallon cask = 144 pints = 81.8 litres, waist-high - rarely seen these days, most older breweries will have a couple kicking around which are useful for saving a trip to the cellar for standard beers at festivals, and about as much as you want to handle on your own in a cellar.
Barrel - don't ask for "a barrel"!!! It has a specific meaning in beer, as a measure of volume of 36 gallons - a handful of family breweries still use casks of that size but these days they are mostly used as tables front of house.
Traditionally a pin is a half-firkin cask in wood/metal, so 36 pints or 20.46 litres. The containers cost about the same as a firkin as fewer are made, so don't expect any discount on the deposit! That led to the idea of a polypin, which is essentially the same as what a homebrewer would call a pressure barrel, a plastic cask of 4.5 gallons.
To complicate things further, some breweries are now referring to 20-litre bag-in-boxes (like wineboxes) as "polypins" as they have some plastic in them and are about the same size as an actual pin. I'm old-school enough to cringe at that usage, but it seems to be quite common these days. Bag in box is a great solution for small parties though, as it doesn't need any dispense equipment.
Kegs are all sized in litres following Continental practice, although some macro breweries will quote eg 11 gallons, which is 50.01 litres. 50 litres is the standard size for returnable steel kegs (sometimes called "Sankeys" after the standard keg fitting), stuff like Carling is often found in 100 litre kegs, the more specialist stuff is found in 30 litres. You pay a premium for beer in keg over cask, typically a 30l keg will cost about the same as the same beer in 9g (ie 40.9 litres) cask.
Newer breweries will use one-way plastic kegs (Keykeg is the most common) which allows them to send beer to bars that are too far away for them to pick up the empties. But they pay ~£15 for the keg, which gets added to the price you pay. And to complicate things further, they have non-Sankey fittings.
Some of the macro breweries still have some 10-gallon kegs left which are now only used for a handful of brands. I think that was a Scottish thing originally, they're pretty rare nowadays.
US imports come in US sizes, usually a sixtel (19.55 litres - named as it's a sixth of a US barrel which is 32 US gallons) or a quarter (29.34 litres) so near enough to 20l and 30l but you hardly ever see those in the UK.
For comparison the classic homebrew Cornelius keg is 5 US gallons = 18.93 litres.
Obviously beer in kegs is filtered and force-carbonated. For casks you have two choices. Obviously CAMRA would love all casks to contain yeast and priming sugar to allow them to carbonate naturally in the cask. But you have to leave it at least 24h (often more depending on the yeast) for the yeast to settle out before serving. Which is fine if you are a pub with a cellar, or have access to the venue a few days before to install the cask. But is out of the question if you aren't allowed into the venue until the day of the event.
For most events that don't have CAMRA purists present, your best bet is brite beer, that has been racked after fermentation to get rid of the yeast so you don't have to worry about disturbing the yeast - you can transport it on the day, throw it around, and then serve it immediately. The only catch is that it has a relatively short shelf life in cask - fine for an event on a specific day, not so good for pubs - as you only have the CO2 left over from fermentation. That in turn means breweries tend not to keep it in stock, so they may need 2-3 weeks notice to do it in cask. This is also where the difference between the senses of "polypin" become important - yeast is fine in a pressure barrel, but a complete PITA in bag-in-box as a gnat's fart will disturb the bag and hence the yeast. But as I say, bag-in-box (with brite beer) is a pretty good option for smaller events.
Pricing is all over the shop at the moment due to the price increases in ingredients versus breweries desperate for sales. In the provinces you're looking at pubs buying direct paying maybe £75+VAT for a firkin (or 30l keg) of trad brown beer, up to £95+VAT for something full of fancy hops. The Southeast generally seems to be maybe £10 more, London may be more still, I don't know. On the other hand you may find someone who brewed with last year's malt in December and is desperate to turn it into cash flow (or a big brewery that is selling at silly prices to kill off the competition).
As has been mentioned, small breweries generally have a weekly delivery schedule that is often published on their "wholesale" page. Local pubs get priority as the core supporters of the brewery so cask-led breweries will often do a main "local" (up to 30 minutes or so away) delivery on Wednesday (so that it could in theory settle and be sold at the weekend) and a smaller one on Friday (for those last-minute orders for the weekend), whereas keg ones tend to do it the other way round. Then on the other days they have a schedule of longer-distance runs of 60-90 minutes away. At least that's my experience, I guess it will be a bit different in London. So as long as you give them a week's notice they can fit you in to the schedule, less than that then they will grumble a bit (but not too much in the current environment, unless you're a long way away...).
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