There are many ways to write the date in BrEng:
(a) the 10th of July[,] 2010 -although it is now rare to see the date written out as we speak it
(b) the tenth of July[,] 2010 - as above (I do occasionally see dates still written out this way in very formal legal documents, eg in property deeds)
(c) 10th July, 2010 - I would say this 'full' version was the most common until quite recently and is still often used - and, indeed, would be my choice if I was writing by hand
(d) 10th July 2010 - not common to have the th/st/rd/nd ordinal 'marker' (is that the word?) but no comma
(e) 10 July, 2010 - not common to have the comma but no ordinal 'marker'
(f) 10 July 2010 - this stripped-down version has become the most common in the age of the computer*
(g) July 10th, 2010
(h) July 10, 2010
The last two are AmEng style, but you do see them in British publications sometimes and in BrEng we do say either:
'the tenth of July' - more common
or
'July the tenth' - but people do often say dates this way in BrEng
In BrEng, we always abbreviate to:
dd-mm-yy, so 10.07.10 or 10/07/10 (or dd-mm-yyyy: 10.07.2010 or 10/07/2010)
unlike in AmEng, where the style is:
mm-dd-yy, so 07.10.10 etc.
So if you see a date written as 10.07.10, you won't know whether it means 10 July 2010 (BrEng) or 7 October 2010 (AmEng) unless you know whether the publication/writer is British or American.
* I don't know why - does anyone know? - but there is a general tendency to remove unnecesary punctuation when writing on the computer - compare 'Dear Mr Bloggs, ... Yours sincerely,' when writing by hand, but 'Dear Mr Bloggs ... Kind regards' (where commas are optional) when writing on the computer.