LNER cashback can also be had on Lloyds, Halifax, Bank of Scotland and MBNA's debit/credit card cashback system ("Everyday Offers"/"Cashback Extras"/"Smart Rewards") from time to time. It does seem to be personalised to some degree based on card data - I don't see LNER on Halifax at the moment, and on my Lloyds account I have zero offers, probably because I've never used the debit card to buy anything, I just have the account for the Club Lloyds freebies. I definitely have seen it some point.
The cashback system that
Fawkes Cat mentions
above for Natwest (RBS do it too) is only accessible on their Reward bank account, which has a £2/month fee (although another benefit of the account is a small rebate of £5/month if you set up two direct debits and open the app every month, so you can actually come out £3/month ahead - it's all about trying to convince people to do their main banking with them, although if you have plenty of direct debits it can be gamed). The company who run it, confusingly just called Reward, I think do have some sort of partnership with Visa - they are mentioned in the terms of Barclaycard Cashback Rewards which is exclusive to Visa cards (so notably excluding the Barclaycard Avios pair), although I have a Natwest Mastercard and have still been able to use it.
The same system is rebranded by a few different banks, most notably Virgin Money, where it's free. (and Barclaycard, as mentioned, where it's also free, and Barclays debit cards, where it is part of the poor value £5/month Blue "Rewards" scheme)
Virgin Money Cashback also has a deal on Virgin Trains Ticketing at the moment - though only 6% and only on your first purchase. (Although VTT itself gives you 1.5% back in Virgin Points and is also currently running a signup offer of 1000 Virgin Points, worth £5 if you redeem for trains)
I will say, even as someone who finds a strange joy in squeezing out every last percent from what are ultimately marketing efforts (to get you to have a certain bank account and/or spend at certain train ticket sellers/retailers) I do find the whole thing quite unfair - realistically every penny saved by people who seek out cashback platforms (or Airtime, or discounted gift card sites, or loyalty schemes like LNER Perks or Club Avanti) comes from the marketing budgets of the TOCs or third party retailers (and retailers of things besides trains, I've even seen supermarkets on Natwest cashback!) and make things more expensive for everyone else, especially people who are less well off and don't have the time to trawl the internet for deals for fun.
And ultimately I really don't think it's a positive for the railway either - train tickets are (for the average person) an inelastic good, that people buy because they need to buy them to go somewhere they need to go; making them 6% or 8% or 10% off doesn't cause more people to buy them I reckon, certainly not 10% more, it just means that when they do the customer pays slightly less and (I imagine) the cashback companies/banks take a small slice so the railway gets even less revenue.
I'd prefer if they just used that money to make trains cheaper - but while they choose not to, I see no reason not to take advantage. I suppose with the Uber scheme at least, it's presumably being financed by their own deep venture capital coffers in an attempt to gain market share, so doesn't cost the railway (and ultimately the taxpayer) anything.
Except one thing - which coming to think of it may be the reason LNER choose to play the cashback game - which is the small % of commission they get by being the retailer who sells the ticket to you. It may well be their real aim is to convince the everyman who usually buys their tickets from the Trainline to pick them instead, then whenever they're not running a cashback deal they get more money? But that's just wild speculation.
