The nursing home won't be left without management in your contact's absence so potentially you could go to the place in person and speak to the manager on duty and see if they're still looking for volunteers. Maybe they could let you shadow a staff member even if they don't have a voluntary position immediately available.
Have a careful read through the admissions website pages for that particular course and see if the experience is just recommended rather than required. If the uni requesting the work experience has specified a mandatory amount of hours and you haven't actually done them it would in all likelihood make you in eligible for that one particular place.
The date you were accepted as a volunteer would still stand and you wouldn't be lying about that, it's perfectly acceptable to say that you made an arrangement and then due to unforeseen circumstances you weren't actually given the hours you had discussed with the manager. It might be worth printing off email correspondence that supports your claims. It's a different case if you "reflected" on your experiences as a volunteer within the personal statement though. I hope that the person that advised you to lie isn't in a position to be dishing out awful advice to other impressionable students.
Do you have anything else you can use for experience form, either through work, shadowing or a different voluntary activity?
Anyway, here's what UCAS have to say on giving misleading information:
"How we verify the information you provide
If we, or a university or college, have any reason to believe that you or your referee have:
◾left out any relevant information, including qualifications you have completed, qualifications with an unsuccessful grade or qualifications for which you are still awaiting results
◾given false or misleading information
we may take any necessary steps to check with you and other parties, including universities, colleges and examination and awarding bodies whether the information you have provided is accurate or complete.
We have the right to cancel your application without refunding your application fee if we determine (having carried out any necessary checks) or have reasonable belief that your application contains false information.
If you have any reason to believe that information we hold about you is not true, complete and accurate, you must tell us.
If we need to verify your identity, we may use details in your application by making checks using any official, publicly available or commercially available identity checking services. If any adverse information is revealed about you we will let you know so that you have an opportunity to respond."