Unfortunately this a problem faced by most. As happymarion said you won't be able to cure the problem in a day, and please don't resort to a soakaway too drastically. It may just need some tlc.
If you look for general lawn care articles these should help. By regularly coreing and piercing your lawn, followed by brushing in some sand or topsoil, you should gradually improve drainage. A secondary problem you may be facing is that; if others around you, like in my situation, have built up paving etc leaving their ground level slightly higher than yours then you will contually suffer from their inconsiderate run-off.
If you can then try and pick a sunnier coner away from any potential problem areas that should help, if you can't match the two up, you may need to consider raised beds expensive as they may be.
Although like everything else where there's a will there's a way, and things are only neccessarily as expensive as you make them.
