Realistic Budget for a day and night in London?

It depends on what you plan to do as to whether £150 is enough, but if I am reading your post correctly, you are just planning to pay for a travelcard and food from your budget, that being the case you should have enough money.

Winter Wonderland is expensive for food,drink, rides etc but free to get in you can just wander around it and soak up the atmosphere and enjoy the lights. London Dungeons will only take an hour and you could go on to do some sight seeing after using your travel card (off peak zone1-2 daily travel card for use on all buses and tubes is £7 per person, so you have £28 for travel during the two days).

I would have a look on MSE restaurant deals site for eating out offers and you have places like Wetherspoons Pubs that do cheap breakfasts and meals. You could maybe look at wandering around somewhere like Camden Market on the Sunday morning. They do some nice mulled wine and hot apple drinks. Covent Garden is also worth a visit as it is good for the street entertainers.

I'd say the best bit of London isn't spending money on stuff and going to attractions as much as chilling out and enjoying the atmosphere, which can be yours just for the price of a coffee

Not sure what you like but the Markets in London are one of the things that people miss / or scare out of towners but are excellent fun for a wander around too, especially in the run up to Xmas.

Camden is the one everyone knows about, but the reason is that it has loads of really interesting stuff to look at antiques / clothes/ funny ethnicky bits and bobs - it can get a bit crazy at the weekends but its interesting and atmospheric.

Slightly more sedate is Borough Market near London Bridge its the big 'foodie' market in London, so very "Nigella" but very interesting, if you're in the area for the london dungeon its worth a look and if you're passing Monmouth Coffee - stop and buy one - its seriously some of the best coffee you can possibly buy and cheaper than a starbucks!

On the lazy sundays I've been at a loose end I've often gone for a wander around up brick lane (buy a fresh bagel from either of the shops at the top of the street) and up into the area around the Truman Brewery which turn into another big market on Sundays, being in the east its a bit hipper and more arty than Camden but has really interesting vibe and is excellent for people watching

The Other Sunday favorite is going for a wander around Hampstead, its really beautiful and really interesting to peek through people's curtains and see how the other half live - and has lots of nice shops and places for a coffee or a cake, and most notably the heath and Parliament hill where you can look out over one of the best views in London (its totally romantic if you're in the mood!)

Greenwich is also great you can get there on the DLR it has a great park, the observatory / house / maritime museum (all free) and another amazing view, and by the cutty sark there's a pedestrian tunnel that lets you walk under the thames.

On the drinking side of things, cheap beer is a bit of problem in London but it doesn't have to be all trendy bars, there's some amazing historic pubs, like Princess Charlotte in Holboun (a beautiful original victorian boozer), ye old cheshire cheese (one of the oldest pubs in the world) on fleet street and plenty of others, one of the best located for sightseeing is The Moon Under Water on whitehall just down from Trafalgar square next to the Trafalgar Studios theatre - its a wetherspoons and does all the cheap meals - with the exeption of Chips (something to do with the fire certificate, I was told)

As for food, it depends what you're into; "cheap" eats in the west end is a bit of a misnomer but it is possible with a bit of planning / know how

Most of the places in the west end are chains; good of you have a voucher but pretty pants without it, so if you're in the market go with a pocketfull of all sorts of vouchers and take your pick!

Don't be put off by fancy restarants though; Some of the fancier ones can give you a really excellent lunch for the same price as a chain if you go for the set meal; so if there's a chef you like off the telly or somewhere you'd really fancy going they could be more affordable than you think - just avoid the wine / ordering off menu and expect to pay abour 10% service charge and you're golden - and don't be worried about being cheap / under dressed - they're they're just a business like any other (just remember there's no need to tip if you've paid for service).

If you're feeling adventurous there are cheap eats in London but you generally have to know where to go, and go out of the west-end I live some of the time off Green Lanes in Harringey which has masses of Turkish resturants - which are cheap and excellent as they're for everyone not just tourists - (my favorite dinner is lacmacun - a small turkish pizza that goes for £1:50 each to take away from a resturant a few doors from me! - so dirt cheap!) - if you're really into a specific type of food there's a restaurant that serves it - so have a look around whatever neigbourhood give it a go - if you cant decide, look for the busiest and with a good mix of people that look like they come from the place the food does - is a good sign, if you're unsure about anything on the menu ask the waiter /waitress or have a look around at what other people are eating and point!

London on £150 for a weekend can give you all sorts of fun, it just takes a bit of planing and prep and a bit of insider knowledge and you'll have a great time