The call button with mobile phone alerts or fall sensor watch will send an alert to your mobile phone when the call button is pressed, but the user will not know that you have received the message. Reassurance could be provided by phoning the person back (if they don't answer this could indicate that they have fallen).
An alternative would be a community alarm system, read more on page 13 of this Age UK fact sheet - "Community alarm systems allow you to be linked up 24 hours a day to a central service offering help in an emergency. The link is usually by telephone, pull cord, pendant worn round your neck, or a combination of these. If you need to summon help urgently and are unable to make a normal telephone call, you can use the pendant, pull the cord or use a special button on the telephone to contact a control centre. This centre has people who talk to you, find out what you need and summon help as appropriate".