The online checkers say a very slow speed is available, but the previous resident got a lot faster?
The online checkers take time to update, sometimes a week or more when the person whose name the telephone line is in has changed. This can result in slow speeds being estimated on the online checkers. If you can find out from the previous resident what their actual broadband speed was, you should be able to achieve the same. The online speed estimators where you put in your telephone number or postcode do nothing to actually limit your broadband speeds. If the checker is wrong your broadband modem will still negotiate the best speed possible for the parameters that have been set.