When you plug in headphones, the plug pushes a switch inside the headphone socket, which breaks the speaker circuit. The switch is actually nothing more than a springy piece of metal, which is meant to return to the 'speakers on' position when you remove the jack. However (either through wear and tear, or just because it's a poor quality component in the first place) that piece of metal can lose its springiness and fail to return to the correct position when you remove the headphone jack, leaving you with the internal speakers permanently disabled. So a dodgy headphone socket might well be the cause of your problem.
However, before seeking a repair for the socket, it would be well to check that it's not actually a software problem first:
Start by right-clicking the speaker icon, at the bottom right of your screen, and selecting 'Open Volume Mixer'. Look beneath the sliders to check that nothing is shown as muted.
Then go to Start > Control Panel > Device Manager.
Click View > Show Hidden Devices
Click the arrowhead to the left of Non-Plug and Play Drivers
Double-click on Beep
Click the Driver tab
Check that Status is shown as Started. (If it's not then, obviously, start it).
If you don't encounter any software problems then it would seem most likely that you need to replace the headphone socket. It's possible to do it yourself (with help from Youtube) but it's a rather fiddly task. It might be better to get a professional to do it for you (after, of course, confirming that it's actually the socket which is at fault) but don't even consider going to PC World! (They charge a flat fee of £50, plus parts, for laptop repairs and there's definitely not fifty quid's worth of labour involved in the task; it should only take a few minutes to do).