Yes the weather has been very different here lately, we've had snow too. Usually the trees are covered with leaves and blossoms now, but many are still bare, it's been wndy and there's been a lot of flooding around the UK too. Some days it's sunny, others it's cold and/or rainy. It's not very predictable right now.
When in England remember that we don't use the Euro much and that the Euro is higher than the dollar, but the pound is higher than both so make sure you have enough currency to begin with or your credit card because if you buy pounds with dollars here you will lose out. However, the Post Office branches do free currency exchange but because of that, they have less favourable rates, or you can go into travel agents, which should cost less in commission than regular Bureau de Change outlets. There are ATM machines aplenty if that is how you are going to get your money, but always check to see if it says it will charge you a fee, because some do charge and you don't want extra charges on top of what you card holders might already be charging to take out money abroad.
London is expensive, very expensive, but there are a lot of free places to go but mainly include museums, galleries, free classical music/drama shows and other educational/historic sites, so if that's not your thing, you will have to spend. There are a lot of 'buy one get one free' (bogof) deals though and things like cut price deals for shows and restaurants, check online for those and which ones are best for your budget. Also, check out the websites for the places you want to go so you can see the ticket prices and then see if you can get some cheaper on eBay or promotional sites.
Even though London has tons to do, see and incorporates multi-cultural influences, it also means that it is busy. Think Christmas shopping, but everyday. So, avoid travelling between 8-10am and 4-7pm because those are the busiest times, it's ok if you don't mind being herded like people to do cattle. Basically, be where you want to be by those times and travel to other places around them.
Get a travelcard if you don't already have some kind of tourist pass. You can get daily, weekend and weekly ones - if you're buying a daily one, buy it after 9.30am, it will be cheaper. That will allow you to travel unlimitedly on the underground, on overground trains and buses in selected zones that you choose with the time limit of the card. So in addition to having a map, get an underground map (free from underground and train stations):
http://www.mtsn.org.uk/files/tube%20colourmap.gif
There are 6 zones on the underground and overground but 4 for buses. Do not take black/red cabs - they will cost you and arm and a leg unless you are going a really short distance, but at the same time don't get into non-licensed cabs just off the street, real ones will have a street business store to walk into and book one.
You are generally likely to get more for money in regards to food in pubs and readymade ready-to-eat in supermarkets. For shopping, you can either check out the millions of stores (which are mainly side by side on streets rather than in mall type buildings) or check out the market scene. We have many market areas, some are really expensive but that tends to be antiques areas, and others which go from low-medium budget i.e. Camden Town. It's an alternative part of London with various markets, shops and lots of multi-cultural food. There are a lot of goth, punk, emo, vintage and unique items there.
There are also a lot of parks here if you want to relax and when it's sunny it can be really nice. Some of the bigger ones have fun fairs, botanical areas, live shows/music etc.
You should be able to travel by train to most places in England and onwards throughout the UK from London, just check which station you need to leave from. Those big stations have tons of shopping and eating facilities inside but they will be generally be more expensive but will also have smaller branches of supermarkets.
Look in the opposite directions to what you are used to when crossing the road
if you crossing anywhere other than at a traffic light. If you use the buses, there will be areas that are priority for older pensioners, people with disabilities/wheelchairs, pregnant women, people with small children/prams and people lots of shopping/baggage. In those areas, if someone comes along that fits into one of those categories, offer your seat to them, or avoid those areas and sit in the other general areas - of course if those priority areas are full it is still polite to offer your seat to someone who needs it more. Also, people try not to look at each other on public transport unless they are being rude or leering.
Pigeons - many people love them, many hate them. Fact - they are not disease ridden, they don't have saliva so carry much less contagious disease in comparison to humans, cats and dogs. You are far more likely to catch something off the people on the streets or public transport, especially in the areas where people put gum everywhere or who breathe/sneeze/cough near you. There are lot of devices in London used to harm pigeons, so you will see many with mutilated feet struggling to walk and looking for food.
Remember to carry tissue, London is very congested, so many people end up with 'black bogie' i.e. when you blow your nose, it might be grey/black. Blow your nose as soon as it needs it.
Other than that, London is full of tourist attractions, pubs, bars, clubs, hotels/B&B's, cultures, students and interesting architecture.