Hello, baby linguist here who will be answering from a linguistic perspective. What I'm writing from here on will assume that you're talking about England in the late 800s, as that's the time period Wikipedia says The Last Kingdom is set in.
I suggest reading this for a good explanation of the different stages involved in becoming able to read.
the bishop says it's too late for his father to learn
It's likely poetic licence. (Though I've never watched the show.)
Wouldn't it take merely a few days to learn to read haltingly, if you already knew most of the vocabulary used?
Nooooooo. I would say at least a month, at the absolute best. How long did it take you to read? Was it easy? No, of course not, it took you years - and you were learning it from a young age, and you were immersed in a modern schooling system for years and years, and you had caregivers who were literate themselves helping you. Think about everything involved. First, you have to learn to recognise the letters. Then, you have to learn what sounds the letters represent. You might think this is easy, but you're coming from a background where functional literacy is expected and supported. People in 800CE who could read were the exception, not the rule. People in late 9th century England didn't write using the Roman alphabet. Their alphabet, the runic alphabet (that image plus a few more characters, see previous link) had just been replaced by the half-uncial script. Given the time frame, if you wanted to read, you would probably have had to learn both. So, that's two separate alphabets to learn. Seriously, look at the runic alphabet. Even assuming you spoke Old English, could you have learnt to read that in a few days, haltingly or no?
was it because spelling back then was as hard as English spelling due to lack of standardization? shouldn't it be extremely easy to learn to read if the spelling system is not akin to English?
I assume you're referring to English's spelling exceptions and weirdnesses. Some languages have spelling systems that are better correlated to the pronunciation of words, like Spanish. Some languages, like French and English, have ones where there's a lot of difference between spellings and sounds. However, a great deal (but not all) of English's spelling weirdness comes from what is called the Great Vowel Shift, which occurred from approximately 1400CE-1600CE, and towards the end of that period is when English spellings were being standardised. This is where the pronunciation of all the long vowels changed, including for words like mouse and goose. So if someone is learning English in the late medieval period (say 1450CE for argument's sake), the spellings will not be standardised but will be much better correlated to pronunciation. Also note there was no "English" as you know it back in 800CE. What everyone spoke in 800CE is (now) called Old English, or, as the people who spoke it called it, Anglisc. It had strong correlation between sounds and spellings.
I can see little kids finding it hard to learn to read, they barely know how to speak properly
TL;DR: The child doesn't just have to learn language, but also all these weird and counterintuitive rules that we, as adults, say are "how English is". What you think is "proper" or "correct" in language is actually the result of years of learning and the application of lots of exceptions. For instance, if a small child (let's say age three) learns a verb, 'try'. They learn that try = present tense (I try), tried = past tense (I tried) and tried = past participle (I have tried). When they learn how 'try' conjugates (changes according to tense), they also learn the following rules: bare verb = present tense, verb+ed = past tense and verb+ed = past participle. We will call this Rules Set 1. Now let's say the child learns another verb, 'speak'. The child will immediately apply Rules Set 1 to speak, and come up with speak, speaked and speaked. This is (to you and me) not correct, and we will immediately tell the child, 'No, it's speak, spoke and spoken'. But why? The child has perfectly acquired Rule Set 1 and applied it. Their conjugation is more logical and is easier to remember. They're still understood. But, we persevere in telling the child they're wrong and the child acquires Rule Set 2: bare verb = present tense, verb with internal vowel(s) changed to 'o' = past tense and verb with internal vowel(s) changed to 'o'+en = past participle. Now let's say the child learns one last verb, 'run'. The child isn't sure which rule set to apply, so they try Rule Set 1: run, runned, runned. 'No,' we say, 'that's wrong.' Ok, well, obviously it must be Rule Set 2! The child produces run, ron and ronen. 'No,' we say, 'still wrong.' The child now has to learn Rule Set 3... And then when they learn 'swim', Rule Set 4, and then when they learn 'think', Rule Set 5... and on and on and on, and that's just for verb conjugation. For instance, the child will have to learn that when they say 'desks' to pronounce the 's' as an 's', but when they say 'bugs' to pronounce the 's' as a 'z'.
