Are the cost of UK passports going up in price to £300 in October 2017?

The Passport Office already sets prices to cover the full cost. The price has gone up significantly in recent years to cover the cost of interviewing first-time applicants and biometric chips. Actually read the Passport Office Annual Report and Accounts and you find that this is true.

So whoever told you this is talking utter rubbish.

I know they are supposed to be going up in price. Also doctors and professional people who once used to be able to sign your application, can no longer do so, so heaven knows who can sign your application saying they have known you for X amount of years! I very much doubt that the cost will be as high as £300 (unless a fake one on the Black Market)

Gov.UK site doesn't mention any increase at all.

https://www.gov.uk/passport-fees