We previously investigated the compatibility of the {textit{Kimber}}–{textit{Martin}}–{textit{Ryskin}} ({textit{KMR}}) {textit{unintegrated}} parton distribution functions ({textit{UPDF}}) with the experimental data on the proton (longitudinal) structure functions ({textit{PSF}} ({textit{PLSF}})). Recently {textit{Golec-Biernat}} and {textit{Stasto}} ({textit{GBS}}) demonstrated that the differential version of {textit{KMR}} prescription and the implementations of angular (strong) ordering ({textit{AOC}} ({textit{SOC}})) constraints, cause the negative-discontinuous {textit{UPDF}} with the ordinary parton distribution functions ({textit{PDF}}) as the input, which leads to a sizable effect on the calculation of {textit{PSF}}. In the present work, we use the new {textit{MMHT2014}}-{textit{LO}}-{textit{PDF}} as the input and focus on the {textit{UPDF}} behaviors as was raised by {textit{GBS}}. The resulting {textit{PSF}} and {textit{PLSF}} are compared with the {textit{MSTW2008}}-{textit{LO}}-{textit{PDF}} and {textit{MRST99}}-{textit{PDF}} and the 2014 data given by the {textit{ZEUS}} and {textit{H1}} collaborations. The calculated {textit{PSF}} and {textit{PLSF}} based on the integral prescription of the {textit{KMR}}-{textit{UPDF}} with the {textit{AOC}} and the ordinary {textit{PDF}} as the input are reasonably consistent with the experimental data. Therefore, they are approximately independent to the {textit{PDF}} (no need to impose cutoff on the {textit{PDF}}). At very small x regions because of the excess of gluons in the {textit{MMHT2014}}-{textit{LO}}-{textit{PDF}} and {textit{MSTW2008}}-{textit{LO}}-{textit{PDF}}, an increase in {textit{PSF}} and {textit{PLSF}} is achieved. Finally, according to the {textit{GBS}} report the differential version by using the cutoff independent {textit{PDF}} produces results far from the experimental data.