i have to attend a one day event in london in october starts at 10 and ends at 18:00. i'm looking for a cheap way of doing that, bearing in mind the even is at Excel.
Cheapest serious option is likely going by bus.
In a comment to the question a quote is given.
"Megabus advertise Aberdeen To London From £1! Plus 50p Booking Fee. – pnuts"
Search the different bus companies or a site that has all of the more common ones and book as early as you can, when the prices are still low.
Busbud is one such site.
Other cheap and reliable options are sharing rides, with booking options online or by app, where you will pay part of the petrol costs against sharing the car.
Blablacar is one such a site.
Rail travel is mostly not the cheapest option but I find it rating quite high in easy to use, and with both day and overnight travel options you might find a good option.
National rail is the site I use to look for tickets, but I might buy from the actual company running the train.
You can of course seek out flights from all airports near enough for you to the London area, in the hope one airline has a special offer. So many flight search engines I leave it up to you to use the one you like best. Otherwise an online search with the names of the cities and flights will find you tickets or airlines. I would also look for all airlines which are known to be cheap, Ryanair, EasyJet, and all UK national ones.
And one regular here mentions at times to hitch-hike on private flights. I would not know how to get such a flight, other than hanging out with pilots owning or flying for private owners, but you might be able to find a way to get such a flight.
Return options are the same, often when paying for bus, flights and rail tickets going both ways are cheaper than two one way ones, but not always. Other travel options may not offer return transport, so you will be stuck with having to search twice.
The easiest: Take Flybe flight 1361 out and Flybe flight 1366 back.
The cheapest: Hitchhike down to London the day before and sleep under a cardboard box. (But seriously, we cannot answer a question like this without more parameters.)
The website, Rome2Rio https://www.rome2rio.com/s/Aberdeen/London gives start and end locations, times, transport type and cost all at a glance. You can even change the time of day you want to travel. It looks like Coach is the cheapest, but this takes 12 hours. The easiest method is up to you!