Punctuation within quotes

Question

When I was at school I was told that a quote should end with a comma. For example:

"The car is on the road," said Tom.
"No it isn't," replied Dick.
"He's right — it's over there!" said Harry.

However, I've recently been advised that this is not correct, and that the preceding text should read:

"The car is on the road." said Tom.
"No it isn't." replied Dick.
"He's right — it's over there!" said Harry.

I'm specifically interested in British English — can anyone tell me if either/both of these are correct?

EDIT

From the answers below, it seems like this depends on what follows. For example:

"The car is on the road," said Tom

But

Tom said, "The car is on the road."

Is this correct?

Answer 1

I learned the same way you did, and have not seen anything recently to the contrary, in any reputable source. The second way you showed looks wrong. I would ask the person who advised you for a reference ("citation needed").

This page says,

A direct quotation is set off from the rest of the sentence by commas. Do not use a period to end a sentence quoted within another sentence.

This page does not address the question directly, but does show by example that it endorses the style you learned in school, not the one you heard about recently.

Update in response to edited question:

Yes, it's correct that it depends on what follows: the period at the end of the quoted sentence is changed to a comma only if the containing sentence continues after the end of the quote (e.g. with a dialogue tag like "said Tom"). If the containing sentence ends with the quote, both are terminated by the same period, which is inside the quotation marks.

Btw, your example

"The car is on the road," said Tom

is missing a final period (after Tom). I think this was just a typo, but I thought it worth mentioning in case that was actually part of your "Is this correct?" question.