I replied in the other thread you made on this topic. In case you didn't see it there, you need to talk to your supervisor at university first and foremost about obtaining ethical approval from your university's research ethics board. Walking into a hospital waiting room where you are likely to encounter unwell and possibly distressed people without even giving them a heads-up beforehand would never be allowed by either your university or the hospital. You will need to come up with a sensitive way of recruiting participants that respects their confidentiality and takes all the costs and benefits of the project into account. Your supervisor can advise on the study design. You will need a solid research proposal before you even approach the hospital, to show them you've thought about all this.
My PhD research is with severely traumatised children and some of it is taking place in a day patient setting. Before I could go into the psych unit I had to have my study design approved by the ethics panel to make sure that I was putting the patients' interests and wellbeing first. It was a very long and laborious process, as shiggydiggy has said. It may be worthwhile thinking of how you could recruit participants without needing to go into a hospital, in case you don't have time to arrange it - an online questionnaire would be a simpler way, which you could post on forums for people with various disabilities or illnesses that have necessitated hospital admission. If you only want to focus on the A&E experience, asking to place a recruitment poster in your GP surgery might work out (although you will need to discuss that with your university too before you do it - I can't emphasise enough how important this is, your university could be in serious trouble if something goes wrong when you're researching with a vulnerable participant group and it turns out you hadn't followed the steps you were supposed to).