The original paper1 explains how the prints were dated:
Here we report on a footprint surface found in Early Pleistocene estuarine muds at Happisburgh, UK, [...] The estuarine sediments at Happisburgh are part of the Hill House Formation (HHF) and are Early Pleistocene in age, dating to between 1 and 0.78 My.
In other words, the footprints were made in mud which subsequently fossilized. The mud is dated geologically2.
Some of the same researchers presented strong dating evidence in another article on Nature3.
The age of the human occupation is constrained by a combination of palaeomagnetism and biostratigraphy.
Palaeomagnetic analyses at Happisburgh were undertaken on 45 samples from the laminated silts (beds A, C, D and F) below, within and above the artefact-bearing gravels (Fig. 3). [...] The Happisburgh sediments therefore display a reversed polarity, depositional remanence throughout beds A, C, D and F (Supplementary Information 3, Supplementary Fig. 1 and Supplementary Table 1). This indicates deposition during either the Matuyama chron (2.52–0.78 Myr) or during a brief Brunhes chron geomagnetic excursion.
The age of the site is further constrained by biostratigraphic evidence. [...] The overlapping ranges of the plant and mammalian taxa indicate a date towards the end of the
This evidence together with the palaeomagnetic data indicates that human occupation occurred towards the end of the Matuyama Chron between 0.99 and 0.78 Myr ago (Fig. 5).
Therefore, the evidence is very convincing that these footprints are, in fact, as old as claimed.
1 Ashton N, Lewis SG, De Groote I, Duffy SM, Bates M, et al. (2014), Hominin Footprints from Early Pleistocene Deposits at Happisburgh, UK. PLoS ONE 9(2): e88329. doi:10.1371/journal.pone.0088329
2 Glad You Asked article, Survey Notes, v. 30 no. 1, September 1997
3 Simon A. Parfitt, Nick M. Ashton, Simon G. Lewis, et al. (2010), Early Pleistocene human occupation at the edge of the boreal zone in northwest Europe, Nature 466, 229–233 (08 July 2010) doi:10.1038/nature09117