I think you are misunderstanding how the market works slightly!
Even if you submitted 2 market orders for the same ticket through the same broker there is no guarantee that they would be filled for the same price - they would both be filled at the best execution price available which could differ for two orders.
For example, you placed two orders each of 1 share using the same broker one after the other. The first to market gets filled at say £1, the second order is an entirely separate transaction and no one may be willing to sell at £1 any more so it might now be £1.01.
That is a very simple example and the likelihood is that stocks will have a much higher liquidity which would make the scenario less likely but equally depending on the stocks the price might be much more volatile so again you could have a difference in fill price between the two orders.
As others have said if you want to lock in a particular price you need to use limit orders. It makes little difference to t212 what price you pay as they just fill at the best price they can (they don’t benefit from a spread).