How much more expensive is it to get bus or train tickets on the day of travel in the UK?

Prices are all over the place in the UK. Having said that, according to thetrainline.com (generally the best source of UK rail tickets online), a standard single in advance (i.e. one way) will cost you about £15. Buy one right now and it'll cost a little more than twice that.

(Note: my figures assume that a ticket bought online for travel this evening costs roughly the same as a ticket bought on a Saturday morning for travel sometime later that day. I think the costs are roughly the same.)

Yes, same day fares are a great deal more expensive. You can get tickets that are valid for any (or most) services on a particular day, so even if you miss one, you can catch the next. They are usually just a bit more expensive than tickets for a specific time, if you book in advance. I usually buy from http://www.thetrainline.com/.

I've always bought my UK bus tickets day-of and had no (meaningful) price differential. I've never gone Birmingham-Manchester. It's possible you can get super deals by buying things well in advance, but I wouldn't sweat it—just check the schedules in advance to make sure the timings work at all. Flexible train tickets have, in my experience, been about the same price all the time, from far-advance to day-of. This includes Eurostar. I would aim to buy train tickets a bit in advance but mostly just to make sure I get a seat: I wouldn't worry too much about price hikes. Of course what you could do is check online to see what's available for today/tomorrow (mutatis mutandis for the actual day-of-week of your arrival) and see how the prices are.

Train: Will you need a return journey in the future? If not, an "off-peak single" would be the ticket type you'd buy at the station on the day. It looks like this is £33.80. "Advance" fares (which are for specific trains only) are £13-15. It looks like you will need 2 train changes, which will be a bit of a pain with luggage. Bus/Coach: Don't discount this as coach journeys in the UK are often cleaner, more comfortable, and easier with luggage than the train. The downside is they are often slower, but not always. Looks like National Express from Birmingham Airport to Manchester Airport usually requires 1 change (although there is at least 1 direct service on a Saturday) and takes around 3 hours. It looks like the "economy single" and "standard single" for this journey are both around £13-14 and both are "amendable and refundable".

le morte de bea arthur has it. If you do buy an advance ticket and you are delayed for whatever reason then, in principle, the conductor can levy a penalty if you don't get the particular train your reservation is on. In practice though, the conductor is unlikely to care. Just say "sorry, I know this isn't my train, but my flight was delayed" as you hand them your ticket. This is what I always do when leaving UK airports — I just figure out what train I will get if my flight arrives on time and book in advance on that. Never had any trouble. The only times I have ever seen advance ticket reservations enforced is on commuter trains leaving/arriving London during the rush hour. I would be staggered if you had any trouble with this if you have a foreign accent, airport luggage, and you're travelling between airports stations on a Saturday.

I've checked thetrainline.com for your route. If you wanted to travel tomorrow, so you couldn't get an advance ticket, the cheapest ticket is a £33.80 http://www.nationalrail.co.uk/times_fares/offpeak.html, which you can buy in the station before you board the train. It's not for a specific train. If you don't want to be restricted to off-peak trains, an Anytime Single ticket costs £37. On the other hand, if you book a ticket a month in advance you can get an http://www.nationalrail.co.uk/times_fares/advance_conditions.html for £15.50. It's for a specific train. Only a limited number of Advance tickets are available, so the closer to the date you get, the more likely they'll be sold out. If you order advance tickets online, there's sometimes a postage fee - although some stations you can pre-book tickets and pick them up from a ticket machine.

If you don't want to be restricted to off-peak trains, an Anytime Single ticket costs £37.Saturday is off peak. Paying extra for Anytime would be a waste of money.If you order advance tickets online, there's sometimes a postage fee - although some stations you can pre-book tickets and pick them up from a ticket machine.You can't get tickets delivered outside the UK. Your options to get the ticket depend on the route/operator. On some routes they will give you a PDF to print, on others you have to collect from to the fastticket machines that are now at pretty much every non-tiny station in the UK. The full list of stations that have these machines is listed when you purchase, but it certainly includes Birmingham International and Manchester Airport.

Thanks to all for the responses. peanut butter milkshake, I won't be coming back on this route. caek, I will probably book the most likely train and run the risk. An Irish accent should be foreign enough.