What would cause poor accuracy in and old bsa meteor

We would need more detail to help you diagnose an accuracy issue, the sorts of details that you would likely only be able to supply if the rifle were in hand. However short of some absurd abuse like shooting sand-covered BB's from it, the problem will not be a worn out barrel. It just doesn't happen with airgun barrels the way it does with powderburners. Most airgun accuracy issues can be solved with little or no cost provided you are tenacious enough to chase it down.
 
In their day the BSA Meteors were nice lower powered air rifles, suitable for people of all ages. But they are getting old now, and like as not have been pulled apart and fiddled with on more than one occasion. All this tampering can take its toll on the old gals.

The good news is that there are plenty of parts still available and most issues are fixable. 

https://www.gunspares.co.uk/categories/23960/Airgun-spares/

I hope this helps.
 
Poor accuracy is a very broad description, could be something simple or something involved. All the parts are pretty much available for them in the UK and not super expensive. You just need to figure which version you have by the serial number. Also ARH has a spring available for it if needed. Installing the new spring in a meteor can be a challenge. 

These were never a high dollar airgun and the build quality reflects that philosophy. As previously stated by someone else the triggers aren't the greatest either. Keep in mind these are low power, about 7-8 ft lbs and meant to stay that way. Mine is .177 and an accurate gun all things considered. Have fun!