If the two were from a single police force you could ask them to treat it as a continuous single offence. If they agreed you would be offered a course or fixed penalty. I think it would be unlikely to succeed in view of the distance apart the offences occurred. There's nothing to stop you asking South Yorkshire police if they would make the same consideration, though I doubt they'd agree.
This leaves you with the option of declining an out-of-court disposal and having the matters heard in court. You can make the same argument there (a single continuous offence) or you could argue that they were two separate offences but were committed "on the same occasion". There is no definition of this but if he court found in your favour you would have two convictions, two fines (and "victim surcharges") two endorsements, but only one lot of penalty points.
Looking at this pragmatically, if you accept two out-of-court disposals from the police they will probably offer you one course and one fixed penalty. This will see you with total costs of about £200 together with one endorsement and three points.
If you go to court the best outcome you can hope for is that the court agrees it was one continuous offence. The result of this (with you being sentenced in accordance with the normal guidelines) is a fine of half a week's income, reduced by a third for a guilty plea, so a third of a week's income. You will also pay a surcharge of 40% of the fine and prosecution costs of around £90. So even if the fine was calculated at just £100 (meaning your income was just £300 per week) it will still cost you £230. You will also have three points imposed.
Remember that is the very best you can hope for and it relies on the court agreeing that you committed one continuous offence. If you fail with that argument (which I believe is highly likely) it will cost you twice as much (although the prosecution may ask for only one lot of costs). If you fail with the second argument as well (two offences committed on the same occasion) it will cost you twice as much and you will also see two endorsements and six points.
In summary, unless you can get the police to treat them as a single offence, going to court would be more costly whichever way it pans out, and in all probability, very much more costly, both in £££s and points.
Don't forget that whatever correspondence you enter into with the police, you must still respond to the "request for driver's details" within the time allowed.