ONS Covid blood test shows Jab "worked"

I have been taking part in in a regular survey by the University of Oxford/Office for National Statistics (ONS). I had been randomly selected for this survey. Since October 2020, every 4 weeks, I have had a nurse visit my home for me to have Covid Swab test and a blood test. 

Every test was previously negative for Covid infection and any Covid antibodies. 

On March 14 I had the Oxford/AstraZeneca first jab at a local NHS vaccination clinic. Luckily I had no side effects apart from a slightly sore arm for a day or two. 

Then on April 1st, I had my ONS 4 weekly swab and blood test. The swab test came back negative for infection but last week I received the result of the blood sample, which showed I am now "positive" for Covid antibodies. 

This suggests that the jab I had on 1 April has "worked" and resulted in me having "antibodies" which could fight off any future Covid infection. The negative swab check on the same day as the positive blood test suggests this but I assume that there is a slim chance, that I could have been infected with asymptotic Covid during the 4 weeks beforehand but it seems unlikely. 

NOTE big time the disclaimer above that just because you test positive for antibodies "Please do not assume you cannot get coronavirus again....."  We do not know how long vaccinations will work but roll on my second jab (due on 1 June) and keep following official advice on social distancing and the other official restrictions until we have all been "jabbed".