Assuming it is a genuine pop up, and not a "click clack" then:
1. If you have access underneath the basin, try pushing up the rod which operates the pop-up.
2. Use a rubber "sucker", like the things you get to hang fittings on tiles. Push over the plug and pull up.
3. Get the water out and see if you can get an ice cube (you'll need lots) to freeze to the plug and pull up.
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local