yes to what everyone else has said
they cannot deny you a homebirth though they will try to make you think they can by using words such as 'allowed' etc only you can decide whther you allow yourself a homebirth.
I have been facing similar problems myself i.e iron levels the link mervs mum linked to is great for factual info on anaemia and all the other reasons they will try to say you can't have a homebirth. What are your haemoglobin levels out of interest? I bet not even that low!
NICE GUIDELINES- https://www.nice.org.uk/nicemedia/live/11837/36280/36280.pdf SAY hb of below 8.5 at onset of labour means increased risk and should be advised to give birth in obstetric led unit (again note the langauage is 'advised' not 'made to')
hb of 8.5-10.5 and in your case clinical or ultrasound suspicion of macrosomia which means estimated bw of 4.5kg or more then individual assessment shpuld be made when planning place of birth (i.e you are informed hopefully with factual clinical information of any risks that could occur becasuse of these 2 things! and you make your own decision based on what you feel is right.
How big are you measuring? do you feel this baby is a lot bigger than your previous babies? as others have said scans are infamously inaccurate for predicting fetal weight can be as much as 25% out either way!
Just remember it is your decision alone to make to not let anyone railroad you into anything just arm yourself with the facts so you feel you have come to an informed decision.
If you continue to face opposition then you should write a strongly worded letter to the head of midwifery or even arrange a meeting with her/him this will almost always sort things out, best of luck let us know how it goes.