Money can be tight, especially these days. If you get hit with a bit of bad luck, it can make things worse. But remember that tons of people have had these problems before, and they survived.
I graduated from College in December, and I STILL haven't found any jobs in my area of expertise. I am down to about $20 a week.
With budgeting and saving, it can really help. (Not trying to sound preachy...).
With that in mind, be creative with your ideas. Do some art.
What talents do you have? Improv Comedy clubs, if you know where to look can be inexpensive. Just look around. you like music, go to a cheap jam session, and then YOU can jam, have fun, and be impressive at the same time.
Movies... Depending on where you live, this can cost roughly $10 a ticket... $20 so far. Not too bad. (Just don't eat the food... THAT'S where the cost adds up. Eat beforehand... get some candy from a Grocery store and sneak it in. Last time I went to a movie, I paid 7.00. (I'm a student) and I bought the same pop at a nearby cafeteria... I save 5 bucks.
Rent a movie. Those are usually cheaper, and it allows for bathroom breaks, and you can rewind the movie if you were too busy gettin' frisky with your lady friend. Just make sure where you live is clean, and looks decent.
Picnics are cheap, just as trajhenkhet said. Plus, you have the romance, and in the summer, it's nice and warm out. Make sure it's not too hot outside, and you have some shade nearby. Most parks allow picnic baskets, but you might want to make sure, you could call them and find out.
Riding the bikes. It's healthy, it get's the heart pumping, and you usually feel better.
Go Karts. It's cheap, and it's fun.
Fireworks... go find a great park, and then you can combine that with the picnic idea. Since there are a lot of families, you may lose a little of that privacy. But because it's a good family event, it's usually cheap so people can get the kids and the big groups in.
Just being together can work. And if this woman likes you, and you like her, I wouldn't think she'd object too much. try not to worry about it... just think about how you can enjoy that time together and do something cheap and fun.
All this also depends on where you live. The cost of Living in California is about 3X as much as the cost of living in Michigan. Canada is cheaper. You live in England, and it's going to be VERY expensive too. You know the best spots already for where you live. Just be creative.
Good luck.