diff --git a/wagtail/core/blocks/base.py b/wagtail/core/blocks/base.py
index 1beb5463dd..8adb22f731 100644
--- a/wagtail/core/blocks/base.py
+++ b/wagtail/core/blocks/base.py
@@ -47,6 +47,12 @@ class Block(metaclass=BaseBlock):
         classname = None
         group = ''
 
+    # Attributes of Meta which can legally be modified after the block has been instantiated.
+    # Used to implement __eq__. label is not included here, despite it technically being mutable via
+    # set_name, since its value must originate from either the constructor arguments or set_name,
+    # both of which are captured by the equality test, so checking label as well would be redundant.
+    MUTABLE_META_ATTRIBUTES = []
+
     """
     Setting a 'dependencies' list serves as a shortcut for the common case where a complex block type
     (such as struct, list or stream) relies on one or more inner block objects, and needs to ensure that
@@ -121,6 +127,16 @@ class Block(metaclass=BaseBlock):
         if not self.meta.label:
             self.label = capfirst(force_str(name).replace('_', ' '))
 
+    def set_meta_options(self, options):
+        """
+        Called when this block is used as the top-level block of a StreamField, to pass on any options
+        from the StreamField constructor that ought to be handled by the block, e.g.
+        body = StreamField(SomeStreamBlock(), max_num=5)
+        """
+        # Ignore all options here; block types that are allowed at the top level (i.e. currently just
+        # StreamBlock) and recognise these options will override this method
+        pass
+
     @property
     def media(self):
         return forms.Media()
@@ -395,9 +411,9 @@ class Block(metaclass=BaseBlock):
     def __eq__(self, other):
         """
         Implement equality on block objects so that two blocks with matching definitions are considered
-        equal. (Block objects are intended to be immutable with the exception of set_name(), so here
-        'matching definitions' means that both the 'name' property and the constructor args/kwargs - as
-        captured in _constructor_args - are equal on both blocks.)
+        equal. Block objects are intended to be immutable with the exception of set_name() and any meta
+        attributes identified in MUTABLE_META_ATTRIBUTES, so checking these along with the result of
+        deconstruct (which captures the constructor arguments) is sufficient to identify (valid) differences.
 
         This was originally necessary as a workaround for https://code.djangoproject.com/ticket/24340
         in Django <1.9; the deep_deconstruct function used to detect changes for migrations did not
@@ -439,7 +455,14 @@ class Block(metaclass=BaseBlock):
             # the migration, rather than leaving the migration vulnerable to future changes to FooBlock / BarBlock
             # in models.py.
 
-        return (self.name == other.name) and (self.deconstruct() == other.deconstruct())
+        return (
+            self.name == other.name
+            and self.deconstruct() == other.deconstruct()
+            and all(
+                getattr(self.meta, attr, None) == getattr(other.meta, attr, None)
+                for attr in self.MUTABLE_META_ATTRIBUTES
+            )
+        )
 
 
 class BoundBlock:
diff --git a/wagtail/core/blocks/stream_block.py b/wagtail/core/blocks/stream_block.py
index 3fd933033d..ed6b060408 100644
--- a/wagtail/core/blocks/stream_block.py
+++ b/wagtail/core/blocks/stream_block.py
@@ -51,6 +51,11 @@ class BaseStreamBlock(Block):
 
         self.dependencies = self.child_blocks.values()
 
+    def set_meta_options(self, opts):
+        for attr in ['required', 'min_num', 'max_num', 'block_counts']:
+            if attr in opts:
+                setattr(self.meta, attr, opts[attr])
+
     def get_default(self):
         """
         Default values set on a StreamBlock should be a list of (type_name, value) tuples -
@@ -381,6 +386,8 @@ class BaseStreamBlock(Block):
         max_num = None
         block_counts = {}
 
+    MUTABLE_META_ATTRIBUTES = ['required', 'min_num', 'max_num', 'block_counts']
+
 
 class StreamBlock(BaseStreamBlock, metaclass=DeclarativeSubBlocksMetaclass):
     pass
diff --git a/wagtail/core/fields.py b/wagtail/core/fields.py
index dfcc17e94e..cc9477d55c 100644
--- a/wagtail/core/fields.py
+++ b/wagtail/core/fields.py
@@ -51,13 +51,31 @@ class Creator:
 
 class StreamField(models.Field):
     def __init__(self, block_types, **kwargs):
+
+        # extract kwargs that are to be passed on to the block, not handled by super
+        block_opts = {}
+        for arg in ['min_num', 'max_num', 'block_counts']:
+            if arg in kwargs:
+                block_opts[arg] = kwargs.pop(arg)
+
+        # for a top-level block, the 'blank' kwarg (defaulting to False) always overrides the
+        # block's own 'required' meta attribute, even if not passed explicitly; this ensures
+        # that the field and block have consistent definitions
+        block_opts['required'] = not kwargs.get('blank', False)
+
         super().__init__(**kwargs)
+
         if isinstance(block_types, Block):
+            # use the passed block as the top-level block
             self.stream_block = block_types
         elif isinstance(block_types, type):
-            self.stream_block = block_types(required=not self.blank)
+            # block passed as a class - instantiate it
+            self.stream_block = block_types()
         else:
-            self.stream_block = StreamBlock(block_types, required=not self.blank)
+            # construct a top-level StreamBlock from the list of block types
+            self.stream_block = StreamBlock(block_types)
+
+        self.stream_block.set_meta_options(block_opts)
 
     def get_internal_type(self):
         return 'TextField'