First you should compare the efficiency of the old boiler with the new one, check the sedbuk page. Then you should check the manual that comes with the new boiler and check what it says about the exact emission values. Then you should get e real heating engeneer or a good plumber to check the emission values with the proper measure instrument. If he/she says that you can't have a printout of these MEASSURED values-good by.
Who has connected the boiler? What does the meassure protocol/report say? It is absolutely necessary to meassure the emission values AND to hand out the written and signed report.
Once you have a real specialist in the house tell him to adjust the pump to meet the demand. A pump can be set at various levels, with just four rads and maybe a tank to feed, the lowest setting would be -most likely- the right one.This would avoid permanent start ups.The efficiency of the Sedbuk system shows the efficiency of the boilers at the stated output.So if your output demand is less than stated output at the boiler you'll get a ping-pong (smiley) rythm, on-off-on-off etc.. This will cause losses at the efficiency rating.
This could be overcome by using a "modulating" boiler. Better a "modulating condensing boiler" and if water mains pressure allows for it then a "modulating combi condensing boiler".
And of course the hydraulic adjustment at the radiators should be done as well, a real plumber would know what to do.
I explained the process here on AAM before, it can be done as a DIY project as well.
Comparing like with like you need to know the energy content in kWhs of the fuel, BTUs are an outdated but still used method to hinder comparison/competition. Check the SEI homepage for "fuel cost comparison" -BTUs aren't even mentioned any more on the fuel cost comparison sheet.