No not at all. Being near-water decreases the chance of sunburn! From a light or UV scenario the claim is false and the NHS is incorrect. Now snow and white concrete are true.
A common misunderstanding I'm afraid Rory. Water is not reflective. Being near a sea or Lake as you state would actually be better than just being outside (Figure 2), all other things being equal.
Water absorbs (https://www.esr.org/outreach/glossary/albedo.html) it does not reflect. You really need to look at UV though.

Here are the rates. Check out water. Virtually 0 reflection!

and here are your sources.
Sample albedos
Surface Typical
albedo
Fresh asphalt 0.04 Pon, Brian (30 June 1999). "Pavement Albedo". Heat Island Group. Archived from the original on 29 August 2007. Retrieved 27 August 2007
Open ocean 0.06 "Thermodynamics | Thermodynamics: Albedo | National Snow and Ice Data Center". nsidc.org. Retrieved 2016-08-14.
Worn asphalt 0.12 Pon, Brian (30 June 1999). "Pavement Albedo". Heat Island Group. Archived from the original on 29 August 2007. Retrieved 27 August 2007
Conifer forest
(Summer) 0.08,[4] Alan K. Betts; John H. Ball (1997). "Albedo over the boreal forest". Journal of Geophysical Research. 102 (D24): 28,901–28,910.
(overall) 0.09 to 0.15 "The Climate System". Manchester Metropolitan University. Retrieved 11 November 2007
Deciduous trees 0.15 to 0.18 "The Climate System". Manchester Metropolitan University. Retrieved 11 November 2007
Bare soil 0.17 Tom Markvart; Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1-85617-390-9.
Green grass 0.25 Tom Markvart; Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1-85617-390-9.
Desert sand 0.40 Tetzlaff, G. (1983). Albedo of the Sahara. Cologne University Satellite Measurement of Radiation Budget Parameters. pp. 60–63.
New concrete 0.55 Tom Markvart; Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1-85617-390-9.
Ocean ice 0.5–0.7 Tom Markvart; Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1-85617-390-9.
Fresh snow 0.80–0.90 Tom Markvart; Luis CastaŁżer (2003). Practical Handbook of Photovoltaics: Fundamentals and Applications. Elsevier. ISBN 1-85617-390-9.
By far the best question you can ask is does UV reflect from water as this is what mostly causes burn. UV is somewhat different than visible light (Figure 3). If you are swimming in the top meter of water you will be exposed to 90% of the UV but out the water this would be 100% and next to the water it would be close to zero, if not zero from the UV hitting the water.
