My survey says the property has problems with the plumbing
This is not unusual. In fact most properties (technically) do have plumbing issues and the older the property - especially period properties - the more problems.
The reason behind this is that laws and regulations that govern plumbing installations are constantly evolving and being updated to make properties safer and longer lasting.
As soon as there is a change in the law or a regulation most properties already built are instantly out of date and so have "problems".
But updates are not normally retrospective - the new law or regulation is for all properties built from that day forward.
Surveyors normally take this into account and will only flag up serious issues such as water piping or drainage at risk of leaking.
But, but, but ... a surveyor is not a plumber. He is only providing a point of view that will need to be checked by a qualified specialist.
To find out if there are real issues you'll need to pay a qualified plumber to go and have a look. Estate agents normally have a few they can recommend.
The plumber will obviously be looking for some work so expect a cost estimate but remember to sort the "nice to have updates" from the "needs to be done as there is a high risk of damage/flooding" work.
Depending on the plumbers report/quote and the state of the market you might consider attempting to renegotiate the sale price with the vendor.
To find out more about how to handle plumbing issues the smart way when purchasing a property pick up a copy of my ebook How to Really Buy a Property.