I'm really surprised that your solicitor is taking such a stance as it is quite common now for indemnity to be taken out against chancel repair. I certainly do for all my clients !
The Law Society Guidelines are that they would suggest that a chancel repair search is carried out for every buyer. The searches aren't great and usually come back to advise there is a potential liabilty and recommend a policy is taken out. This is because there is no specific place to check for liability so it is a bit of a mine field for Lawyers because we can never be sure whether there is any liability or not.
My advice to you would be to take a policy out especially if the house you are buying is built on land previously owned by the Church of England and it dates back to Medieval times as these are 2 of the major requirements for a church to be able to claim liability.
Skywalker is right in that 2013 is a key date but it doesnt mean that Chancel repair liability wont exist after this date. Its simply the date that any churches with liability need to register an entry against the property with the Land Registry.
This means that from 2013 onwards if the property does have a liability it will show up on the Office Copy Entries and it will be safe to assume that if there isn't such an entry then liability doesn't exist.
Hope this helps