The question is about the UK Road code.

Picture this.

There is an intersection between a Major and a Minor road. There two
cards travelling towards each other arriving at the intersection at
the same time, and both wanting to turn down the same road ( ie Both
wanting to travel North ). Ie One is turning left, the other turning
right, crossing the road. Which car has priority and why.

I guess the answer would be the same in this scenario. There is two
Giveway points on opposite sides of a main road, and a car at each.
Both are turning on to the main road and both want to go North. Which
car has priority, and why.

In both cases there are no other cars on the road.

The above may sound stupid, but it is really annoying me.

Dear Kershy-ga

In the UK, road traffic is governed by various Road Traffic Acts and
the Highway Code.

The Highway Code is not legislation but many of its rules appear in
the law. Also ?although failure to comply with the other rules of the
Code will not, it itself, cause a person to be prosecuted, The Highway
Code may be used in evidence in any court proceedings under Traffic
Acts to establish liability.?

Highway Code 122 points out that drivers must not: 

    * drive dangerously
    * drive without due care and attention
    * drive without reasonable consideration for other road users.
      Law RTA 1988 sects 2 & 3 as amended by RTA 1991
http://www.highwaycode.gov.uk/12.htm

It also goes on to request that drivers give consideration to other
roads users and possess adaptability when driving.

So, if there is a cross-road where there are no road markings, then no
person has priority. Courtesy and consideration should lead to one
allowing the other to pass first.

Highway Code 124
?...in side roads and country lanes look out for unmarked junctions
where nobody has priority.?
http://www.highwaycode.gov.uk/12.htm#124


If the cross-roads have Give Way signs or a Stop sign, then the
drivers must obey these laws.

147: You MUST stop behind the line at a junction with a 'Stop' sign
and a solid white line across the road. Wait for a safe gap in the
traffic before you move off.
Laws RTA 1988 sect 36 & TSRGD regs 10 & 16

148: The approach to a junction may have a 'Give Way' sign or a
triangle marked on the road. You MUST give way to traffic on the main
road when emerging from a junction with broken white lines across the
road.
Laws RTA 1988 sect 36 & TSRGD regs 10(1), reg 16(1) & 25 

http://www.highwaycode.gov.uk/16.htm#146


If one of your drivers should pull away first then the other driver
should give way as there is traffic on the main road coming towards
them. However, practically speaking from everyday experience of
driving, if they arrive together at the junction or within a few
seconds of each other, they will invariably politely indicate to each
other who should go first. Code 122 applies.

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder

Search strategy
Personal knowledge as a driver and former police officer.
Highway Code
http://www.highwaycode.gov.uk/index.htm

Thank you very much. A comment was made that New Zealand had such a
rule for the situation i was talking about. i have to say i have never
liked the NZ giveway rules, but at least they where clear to me. I
thought there would be something similar in the UK- and from my
driving experiance i really thought it was the person turning left had
priority but could never find in the road code. thanks again.

Here's my take:

Neither car has priority and it is customary for one driver to
indicate to the other that he/she should proceed.

In other words, the 'usual' courtesies should be observed.

This Wikipedia discussion of the subject for different countries
supports Answerfinder  - of course -  but may add some understanding. 
It seems that you are looking for a rule like the one on the Continent
and in New Zealand that says that the car from the right has the right
of way.
I.e., when two cars approach an intersection, the driver seeing a car
approaching from his right must give way; or in your example of two
cars turning into a crossing road, the one who sees the other car to
his right as he turns left must give way.

A nice, understandable rule, but the UK doesn't have it.

Im a UK driver and I always thought the driver turning left, that is,
not crossing traffic as a right turner would, has priority.
Is the junction like this:
     |
  -- | --
     |
The horizontal lines are minor roads and the vertical line is a major
road, 2 cars come to the junction facing each other on the horizontal
road and want to turn North (up)?
If that is the correct scenario, I would expect the car turning left
to have priority as they are not crossing both lanes. My dad always
see it as the person who has least road lines to cross has priority
but I'm not sure if that always works. If turning left, you have the
double dotted line to cross and that is all, if turning right you have
the doulbe dotted line AND the centre line to cross.
Anyone understand any of that?
Ed

Dear kershy-ga,
Thank you for the tip. Pleased I could help.
answerfinder-ga