Can an assessment be split in two?

Today I had a home visit for my PIP review assessment. The assessor who called didn't even wait and ring our bell, but started walking away before my husband called out to her.

It took an hour for her to go through my various health conditions (I admit they are complex, but I provided plenty of evidence from various consultants etc.) She said she didn't understand why my assessment hadn't been done on paper because there was plenty of supporting evidence.

What did surprise me however was that as we came up to the one hour mark, she said she had to finish there because she had another assessment to do, but that someone else would come and finish my assessment at some point. She said they should have booked a 'double' appointment for me.

Is this actually correct? I can understand if she had to come back, but to send someone else seems needlessly stressful, and surely won't save time because I'm going to have to go through a lot of things again.

I'd be very grateful to hear if this is correct, i.e. that two different assessors can carry out an assessment for the same person.

Many thanks.

Yes, it was Capita. She literally walked up the path to our gate, turned and walked back out again. I'll certainly contact them on Monday about the assessment. She phoned her manager (not her usual one, apparently, who was unavailable) and simply left a message for him.
Thank you so much for your help. Much appreciated.

Update: Rang Capita explained what had happened (including behaviour at the gate).

Was told it was being investigated to see why the assessment was stopped, and to phone them back on Friday (3rd August). I explained that the assessment wasn't 'stopped' but that the assessor ran out of time.

Feel a bit uneasy at the 'spin' on this. Am I being investigated or the assessor? I'll keep you updated as and when I get any news.

uPDATE:
Phoned Capita to be told they had booked me another assessment, this time for two hours at the nearest assessment centre. I explained I had a doctor's letter in support of a home assessment, and that they had accepted this (hence my recent home visit a week ago.) I was told to get a taxi - my arguments fell on stony ground. Everything I said, the response was 'get a taxi' even though I now have IBD and am liable to soil myself (and the taxi).

So I took your advice Gordon and said I wanted to complain. In fairness they wanted full details of what had happened at the first assessment and I gave them this. I did ask though, when they mentioned about it being 'under investigation' who exactly was being investigated? Myself or the assessor. I was assured it was 'the case'.

I stressed to them that the assessor was polite, but that she had clearly intended not to do the assessment, and there was no excuse for not ringing the bell and starting to walk away. I explained I have had other home assessments and none had had this problem.

I also stressed that she was very slow, and there was no earthly reason why it would take a whole hour to note down my medication - she didn't ask a single question about my daily living routine.

I explained that I felt it was hugely unfair that I should have to have three hours of assessment plus was expected to make a long and impossible journey simply because the original assessor had not done her job properly. I was being penalised for her shortcomings.

Eventually, he suggested he would get advice and I would have either another one hour home assessment, a two hour home assessment or a paper assessment.

In the meantime I will get an appointment for a two hour appointment at an assessment centre.